Edit Profile (opens in new tab) Algaba, Antonio Co-Author Distance Author ID: algaba.antonio Published as: Algaba, Antonio; Algaba, A. Documents Indexed: 126 Publications since 1998 Co-Authors: 18 Co-Authors with 125 Joint Publications 508 Co-Co-Authors all top 5 Co-Authors 1 single-authored 59 García, Cristóbal 55 Rodríguez-Luis, Alejandro J. 36 Merino, Manuel 32 Gamero, Estanislao 30 Reyes, Manuel 23 Freire Macías, Emilio 22 Fernández-Sánchez, Fernando 18 Giné, Jaume 12 Qin, Bo-Wei 11 Chung, Kwok-Wai 7 Fuentes, Natalia 4 Checa, Isabel 4 Domínguez-Moreno, María C. 2 Díaz, Maria Elena 2 Llibre, Jaume 1 Maestre, Manuel 1 Ponce, Enrique 1 Teixeira, Marco Antonio all top 5 Serials 15 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 11 Communications in Nonlinear Science and Numerical Simulation 10 Journal of Mathematical Analysis and Applications 10 Nonlinear Dynamics 7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 Applied Mathematics and Computation 6 Qualitative Theory of Dynamical Systems 4 Physics Letters. A 4 Chaos, Solitons and Fractals 3 Journal of Computational and Applied Mathematics 3 Journal of Differential Equations 3 Physica D 3 Mediterranean Journal of Mathematics 2 Nonlinearity 2 Rocky Mountain Journal of Mathematics 2 Acta Applicandae Mathematicae 2 Applied Mathematics Letters 2 European Journal of Applied Mathematics 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Bulletin des Sciences Mathématiques 2 Discrete and Continuous Dynamical Systems 2 Chaos 2 Nonlinear Analysis. Real World Applications 2 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 2 Communications on Pure and Applied Analysis 1 Journal of Sound and Vibration 1 Physica A 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Applied Mathematics and Mechanics. (English Edition) 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Differential Equations and Dynamical Systems 1 Abstract and Applied Analysis 1 Acta Mathematica Sinica. English Series 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms 1 International Journal of Pure and Applied Mathematics 1 SIAM Journal on Applied Dynamical Systems 1 Boletín de la Sociedad Española de Matemática Aplicada. S\(\vec{\text{e}}\)MA all top 5 Fields 109 Ordinary differential equations (34-XX) 61 Dynamical systems and ergodic theory (37-XX) 5 Mechanics of particles and systems (70-XX) 2 Partial differential equations (35-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Biology and other natural sciences (92-XX) 1 Nonassociative rings and algebras (17-XX) 1 Approximations and expansions (41-XX) 1 Numerical analysis (65-XX) 1 Optics, electromagnetic theory (78-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 110 Publications have been cited 1,003 times in 401 Documents Cited by ▼ Year ▼ The integrability problem for a class of planar systems. Zbl 1165.34023Algaba, A.; Gamero, E.; García, C. 58 2009 A note on the triple-zero linear degeneracy: normal forms, dynamical and bifurcation behaviors of an unfolding. Zbl 1043.37042Freire, E.; Gamero, E.; Rodríguez-Luis, A. J.; Algaba, A. 34 2002 Hypernormal form for the Hopf-zero bifurcation. Zbl 0996.37062Algaba, A.; Freire, E.; Gamero, E. 32 1998 Chen’s attractor exists if Lorenz repulsor exists: The Chen system is a special case of the Lorenz system. Zbl 1323.37020Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 30 2013 Isochronicity via normal form. Zbl 1021.34022Algaba, Antonio; Freire, Emilio; Gamero, Estanislao 29 2000 Centers of quasi-homogeneous polynomial planar systems. Zbl 1238.34052Algaba, A.; Fuentes, N.; García, C. 28 2012 Quasi-homogeneous normal forms. Zbl 1022.34034Algaba, A.; Freire, E.; Gamero, E.; García, C. 28 2003 The center problem for a family of systems of differential equations having a nilpotent singular point. Zbl 1156.34031Algaba, A.; García, C.; Reyes, M. 25 2008 Integrability of two dimensional quasi-homogeneous polynomial differential systems. Zbl 1213.37093Algaba, A.; García, C.; Reyes, M. 24 2011 Existence of an inverse integrating factor, center problem and integrability of a class of nilpotent systems. Zbl 1266.37023Algaba, A.; García, C.; Reyes, M. 22 2012 The Lü system is a particular case of the Lorenz system. Zbl 1301.37020Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 22 2013 Some results on Chua’s equation near a triple-zero linear degeneracy. Zbl 1083.93020Algaba, A.; Merino, M.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 21 2003 A tame degenerate Hopf-pitchfork bifurcation in a modified van der Pol-Duffing oscillator. Zbl 0976.70016Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 20 2000 On the Hopf-pitchfork bifurcation in the Chua’s equation. Zbl 1090.34545Algaba, A.; Merino, M.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 18 2000 Computing center conditions for vector fields with constant angular speed. Zbl 1032.34026Algaba, A.; Reyes, M. 17 2003 Analysis of Hopf and Takens-Bogdanov bifurcations in a modified van der Pol-Duffing oscillator. Zbl 0928.70042Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 17 1998 Monodromy, center-focus and integrability problems for quasi-homogeneous polynomial systems. Zbl 1192.34035Algaba, A.; Freire, E.; Gamero, E.; García, C. 16 2010 A three-parameter study of a degenerate case of the Hopf-pitchfork bifurcation. Zbl 0943.34027Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 16 1999 Hypernormal form calculation for triple-zero degeneracies. Zbl 0988.37062Gamero, E.; Freire, E.; Rodríguez-Luis, A. J.; Ponce, E.; Algaba, A. 13 1999 An algorithm for computing quasi-homogeneous formal normal forms under equivalence. Zbl 1063.34029Algaba, Antonio; Freire, Emilio; Gamero, Estanislao; García, Cristóbal 13 2004 Characterization of a monodromic singular point of a planar vector field. Zbl 1226.34031Algaba, A.; García, C.; Reyes, M. 13 2011 Hypernormal forms for equilibria of vector fields. Codimension one linear degeneracies. Zbl 0930.34027Algaba, A.; Freire, E.; Gamero, E. 13 1999 The center problem for \(\mathbb{Z}_2\)-symmetric nilpotent vector fields. Zbl 1395.34047Algaba, Antonio; García, Cristóbal; Giné, Jaume; Llibre, Jaume 12 2018 On orbital-reversibility for a class of planar dynamical systems. Zbl 1337.34039Algaba, A.; Checa, I.; García, C.; Gamero, E. 12 2015 Reversibility and quasi-homogeneous normal forms of vector fields. Zbl 1202.34069Algaba, A.; García, C.; Teixeira, M. A. 12 2010 A bifurcation analysis of a simple electronic circuit. Zbl 1064.34030Algaba, A.; Gamero, E.; Rodríguez-Luis, A. J. 11 2005 On a codimension-three unfolding of the interaction of degenerate Hopf and pitchfork bifurcations. Zbl 0983.37057Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 11 1999 Nontransversal curves of \(T\)-points: A source of closed curves of global bifurcations. Zbl 0999.37035Algaba, A.; Fernández-Sánchez, F.; Freire, E.; Merino, M.; Rodríguez-Luis, A. J. 11 2002 Like-linearizations of vector fields. Zbl 1196.37080Algaba, A.; García, C.; Reyes, M. 11 2009 Characterizing isochronous points and computing isochronous sections. Zbl 1208.34034Algaba, A.; Reyes, M. 11 2009 Analytic integrability for some degenerate planar vector fields. Zbl 1306.34046Algaba, Antonio; García, Cristóbal; Giné, Jaume 11 2014 Analytic integrability around a nilpotent singularity. Zbl 1432.34002Algaba, Antonio; García, Cristóbal; Giné, Jaume 10 2019 A nonlinear time transformation method to compute all the coefficients for the homoclinic bifurcation in the quadratic Takens-Bogdanov normal form. Zbl 1430.37054Algaba, Antonio; Chung, Kwok-Wai; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J. 10 2019 Local bifurcation of limit cycles and integrability of a class of nilpotent systems of differential equations. Zbl 1201.34061Algaba, A.; García, C.; Reyes, M. 10 2009 Nilpotent centres via inverse integrating factors. Zbl 1384.34037Algaba, Antonio; García, Cristóbal; Giné, Jaume 10 2016 Rational integrability of two-dimensional quasi-homogeneous polynomial differential systems. Zbl 1201.34050Algaba, A.; García, C.; Reyes, M. 10 2010 Centers on center manifolds in the Lorenz, Chen and Lü systems. Zbl 1457.34061Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 9 2014 Resonances of periodic orbits in Rössler system in presence of a triple-zero bifurcation. Zbl 1145.37322Algaba, Antonio; Freire, Emilio; Gamero, Estanislao; Rodríguez-Luis, Alejandro J. 9 2007 Takens-Bogdanov bifurcations of periodic orbits and Arnold’s tongues in a three-dimensional electronic model. Zbl 1090.37543Algaba, A.; Merino, M.; Rodríguez-Luis, A. J. 9 2001 A class of non-integrable systems admitting an inverse integrating factor. Zbl 1333.37076Algaba, A.; Fuentes, N.; García, C.; Reyes, M. 9 2014 The center problem. A view from the normal form theory. Zbl 1329.34071Algaba, A.; Gamero, E.; García, C. 9 2016 High-order analysis of global bifurcations in a codimension-three Takens-Bogdanov singularity in reversible systems. Zbl 1436.34035Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 8 2020 Characterizing and computing normal forms using Lie transforms: A survey. Zbl 1001.34030Algaba, A.; Freire, E.; Gamero, E. 8 2001 Invariant curves and analytic integrability of a planar vector field. Zbl 1412.34110Algaba, A.; García, C.; Reyes, M. 8 2019 An exact homoclinic orbit and its connection with the Rössler system. Zbl 1396.37027Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 8 2015 Takens-Bogdanov bifurcations of equilibria and periodic orbits in the Lorenz system. Zbl 1489.37069Algaba, A.; Domínguez-Moreno, M. C.; Merino, M.; Rodríguez-Luis, A. J. 8 2015 Analytical approximation of cuspidal loops using a nonlinear time transformation method. Zbl 1433.37019Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 7 2020 Closed curves of global bifurcations in Chua’s equation: a mechanism for their formation. Zbl 1056.37067Algaba, Antonio; Merino, Manuel; Fernández-Sánchez, Fernando; Rodríguez-Luis, Alejandro J. 7 2003 Uniformly isochronous quintic planar vector fields. Zbl 0976.37026Algaba, A.; Reyes, M.; Bravo, A. 7 2000 On Darboux polynomials and rational first integrals of the generalized Lorenz system. Zbl 1302.34001Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 7 2014 Computation of all the coefficients for the global connections in the \(\mathbb{Z}_2\)-symmetric Takens-Bogdanov normal forms. Zbl 1453.37045Algaba, Antonio; Chung, Kwok-Wai; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J. 7 2020 Nondegenerate and nilpotent centers for a cubic system of differential equations. Zbl 1416.34020Algaba, Antonio; García, Cristóbal; Giné, Jaume 7 2019 Comment on “Sil’nikov chaos of the Liu system”. Zbl 1317.34083Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 7 2011 Study of the Hopf bifurcation in the Lorenz, Chen and Lü systems. Zbl 1345.34069Algaba, Antonio; Domínguez-Moreno, María C.; Merino, Manuel; Rodríguez-Luis, Alejandro J. 7 2015 Analysis of the T-point-Hopf bifurcation in the Lorenz system. Zbl 1329.37082Algaba, A.; Fernández-Sánchez, F.; Merino, M.; Rodríguez-Luis, A. J. 7 2015 On the formal integrability problem for planar differential systems. Zbl 1282.34005Algaba, Antonio; García, Cristóbal; Giné, Jaume 6 2013 Analysis of a Belyakov homoclinic connection with \(\mathbb Z_2\)-symmetry. Zbl 1268.37017Algaba, Antonio; Merino, Manuel; Rodríguez-Luis, Alejandro J. 6 2012 Nilpotent systems admitting an algebraic inverse integrating factor over \(\mathbb{C}((x,y))\). Zbl 1267.34002Algaba, Antonio; García, Cristóbal; Reyes, Manuel 6 2011 Centers with degenerate infinity and their commutators. Zbl 1037.34024Algaba, A.; Reyes, M. 6 2003 Computing simplest normal forms for the Takens-Bogdanov singularity. Zbl 1050.34052Algaba, Antonio 6 2002 Isochronous centres and foci via commutators and normal forms. Zbl 1155.34018Algaba, A.; Reyes, M. 6 2008 A degenerate Hopf-saddle-node bifurcation analysis in a family of electronic circuits. Zbl 1201.37021Algaba, A.; Gamero, E.; García, C.; Merino, M. 6 2007 Analytical integrability problem for perturbations of cubic Kolmogorov systems. Zbl 1404.37021Algaba, Antonio; García, Cristóbal; Reyes, Manuel 6 2018 A new algorithm for determining the monodromy of a planar differential system. Zbl 1334.34188Algaba, A.; García, C.; Reyes, M. 6 2014 Geometric criterium in the center problem. Zbl 1356.34035Algaba, Antonio; García, Cristóbal; Giné, Jaume 6 2016 Analytic integrability for some degenerate planar systems. Zbl 1278.34001Algaba, Antonio; García, Cristóbal; Giné, Jaume 5 2013 Open-to-closed curves of saddle-node bifurcations of periodic orbits near a nontransversal T-point in Chua’s equation. Zbl 1142.34029Algaba, Antonio; Merino, Manuel; Fernández-Sánchez, Fernando; Rodríguez-Luis, Alejandro J. 5 2006 Comments on “Global dynamics of the generalized Lorenz systems having invariant algebraic surfaces”. Zbl 1291.34080Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 5 2014 Comment on ‘Šilnikov-type orbits of Lorenz-family systems’. Zbl 1395.37020Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 5 2013 Analytical approximation of the canard explosion in a van der Pol system with the nonlinear time transformation method. Zbl 1482.34138Algaba, Antonio; Chung, Kwok-Wai; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J. 5 2020 High-order analysis of canard explosion in the Brusselator equations. Zbl 1447.34023Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 5 2020 Analytic integrability inside a family of degenerate centers. Zbl 1354.34005Algaba, Antonio; Checa, Isabel; García, Cristóbal; Giné, Jaume 5 2016 Integrability of planar nilpotent differential systems through the existence of an inverse integrating factor. Zbl 1464.34006Algaba, Antonio; García, Cristóbal; Giné, Jaume 5 2019 Analytic integrability around a nilpotent singularity: the non-generic case. Zbl 1483.34006Algaba, Antonio; Díaz, María; García, Cristóbal; Giné, Jaume 4 2020 High-order approximation of heteroclinic bifurcations in truncated 2D-normal forms for the generic cases of Hopf-zero and nonresonant double Hopf singularities. Zbl 1478.34067Qin, B. W.; Chung, K. W.; Algaba, A.; Rodríguez-Luis, A. J. 4 2021 High-order study of the canard explosion in an aircraft ground dynamics model. Zbl 1459.34133Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 4 2020 Oscillation-sliding in a modified van der Pol-Duffing electronic oscillator. Zbl 1237.34049Algaba, A.; Fernández-Sánchez, F.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 4 2002 Comment on “Existence of heteroclinic orbits of the Shil’nikov type in a 3D quadratic autonomous chaotic system”. Zbl 1247.34072Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 4 2012 Hopf bifurcations and their degeneracies in Chua’s equation. Zbl 1248.34059Algaba, Antonio; Merino, Manuel; Fernández-Sánchez, Fernando; Rodríguez-Luis, Alejandro J. 4 2011 A note on analytic integrability of planar vector fields. Zbl 1268.34003Algaba, A.; García, C.; Reyes, M. 4 2012 Homoclinic connections near a Belyakov point in Chua’s equation. Zbl 1089.37019Algaba, A.; Merino, M.; Rodríguez-Luis, A. J. 4 2005 Geometry of the uniformly isochronous centers with polynomial commutator. Zbl 1231.34052Algaba, A.; Reyes, M.; Bravo, A. 4 2002 A bifurcation analysis of planar nilpotent reversible systems. Zbl 1372.34073Algaba, A.; Freire, E.; Gamero, E.; García, C. 4 2017 Comments on “The Chen system revisited”. Zbl 1306.34020Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 4 2014 Asymptotic expansions for a family of non-generic canards using parametric representation. Zbl 07198686Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 3 2020 Quasi-homogeneous linearization of degenerate vector fields. Zbl 1440.34039Algaba, A.; García, C.; Reyes, M. 3 2020 Homoclinic interactions near a triple-zero degeneracy in Chua’s equation. Zbl 1270.34113Algaba, Antonio; Merino, Manuel; Rodríguez-Luis, Alejandro J. 3 2012 Nondegenerate centers and limit cycles of cubic Kolmogorov systems. Zbl 1390.37082Algaba, Antonio; García, Cristóbal; Giné, Jaume 3 2018 Analytical integrability of perturbations of quadratic systems. Zbl 1481.34003Algaba, Antonio; García, Cristóbal; Reyes, Manuel 3 2021 Superluminal periodic orbits in the Lorenz system. Zbl 1510.34082Algaba, A.; Merino, M.; Rodríguez-Luis, A. J. 3 2016 Analysis of the T-point-Hopf bifurcation with \(\mathbb Z_2\)-symmetry. Application to Chua’s equation. Zbl 1193.34078Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 3 2010 Comment on “A constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family”. Zbl 1470.37040Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 2 2014 Center conditions of a particular polynomial differential system with a nilpotent singularity. Zbl 1478.34031Algaba, Antonio; García, Cristóbal; Giné, Jaume 2 2020 Orbital normal forms for a class of three-dimensional systems with an application to Hopf-zero bifurcation analysis of Fitzhugh-Nagumo system. Zbl 1433.34055Algaba, A.; Fuentes, N.; Gamero, E.; García, C. 2 2020 The reversibility problem for quasi-homogeneous dynamical systems. Zbl 1283.34032Algaba, Antonio; Gamero, Estanislao; García, Cristóbal 2 2013 Quasi-homogeneous normal forms for null linear part. Zbl 1054.34065Algaba, A.; Freire, E.; Gamero, E.; García, C. 2 2003 Analytic integrability of some examples of degenerate planar vector fields. Zbl 1343.34003Algaba, Antonio; García, Cristóbal; Giné, Jaume 2 2016 Comments on “Non-existence of Shilnikov chaos in continuous-time systems”. Zbl 1277.65108Algaba, A.; Fernández-Sánchez, F.; Merino, M.; Rodríguez-Luis, A. J. 2 2013 Structural stability of planar quasi-homogeneous vector fields. Zbl 1405.34047Algaba, A.; Fuentes, N.; Gamero, E.; Garcia, C. 2 2018 Comments on “Dynamics of the general Lorenz family” by Y. Liu and W. Pang. Zbl 1319.37011Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 2 2014 High-order approximation of heteroclinic bifurcations in truncated 2D-normal forms for the generic cases of Hopf-zero and nonresonant double Hopf singularities. Zbl 1478.34067Qin, B. W.; Chung, K. W.; Algaba, A.; Rodríguez-Luis, A. J. 4 2021 Analytical integrability of perturbations of quadratic systems. Zbl 1481.34003Algaba, Antonio; García, Cristóbal; Reyes, Manuel 3 2021 On the integrability problem for the Hopf-zero singularity and its relation with the inverse Jacobi multiplier. Zbl 1510.34074Algaba, A.; Fuentes, N.; Gamero, E.; García, C. 2 2021 Analytically integrable centers of perturbations of cubic homogeneous systems. Zbl 1472.34055Algaba, Antonio; García, Cristóbal; Reyes, Manuel 1 2021 A new normal form for monodromic nilpotent singularities of planar vector fields. Zbl 1482.34106Algaba, Antonio; García, Cristóbal; Giné, Jaume 1 2021 Asymptotic expansions for a degenerate canard explosion. Zbl 1496.34094Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 1 2021 High-order analysis of global bifurcations in a codimension-three Takens-Bogdanov singularity in reversible systems. Zbl 1436.34035Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 8 2020 Analytical approximation of cuspidal loops using a nonlinear time transformation method. Zbl 1433.37019Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 7 2020 Computation of all the coefficients for the global connections in the \(\mathbb{Z}_2\)-symmetric Takens-Bogdanov normal forms. Zbl 1453.37045Algaba, Antonio; Chung, Kwok-Wai; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J. 7 2020 Analytical approximation of the canard explosion in a van der Pol system with the nonlinear time transformation method. Zbl 1482.34138Algaba, Antonio; Chung, Kwok-Wai; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J. 5 2020 High-order analysis of canard explosion in the Brusselator equations. Zbl 1447.34023Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 5 2020 Analytic integrability around a nilpotent singularity: the non-generic case. Zbl 1483.34006Algaba, Antonio; Díaz, María; García, Cristóbal; Giné, Jaume 4 2020 High-order study of the canard explosion in an aircraft ground dynamics model. Zbl 1459.34133Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 4 2020 Asymptotic expansions for a family of non-generic canards using parametric representation. Zbl 07198686Qin, Bo-Wei; Chung, Kwok-Wai; Algaba, Antonio; Rodríguez-Luis, Alejandro J. 3 2020 Quasi-homogeneous linearization of degenerate vector fields. Zbl 1440.34039Algaba, A.; García, C.; Reyes, M. 3 2020 Center conditions of a particular polynomial differential system with a nilpotent singularity. Zbl 1478.34031Algaba, Antonio; García, Cristóbal; Giné, Jaume 2 2020 Orbital normal forms for a class of three-dimensional systems with an application to Hopf-zero bifurcation analysis of Fitzhugh-Nagumo system. Zbl 1433.34055Algaba, A.; Fuentes, N.; Gamero, E.; García, C. 2 2020 Orbitally universal centers. Zbl 1511.34038Algaba, Antonio; García, Cristóbal; Giné, Jaume; Llibre, Jaume 1 2020 Analytic integrability around a nilpotent singularity. Zbl 1432.34002Algaba, Antonio; García, Cristóbal; Giné, Jaume 10 2019 A nonlinear time transformation method to compute all the coefficients for the homoclinic bifurcation in the quadratic Takens-Bogdanov normal form. Zbl 1430.37054Algaba, Antonio; Chung, Kwok-Wai; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J. 10 2019 Invariant curves and analytic integrability of a planar vector field. Zbl 1412.34110Algaba, A.; García, C.; Reyes, M. 8 2019 Nondegenerate and nilpotent centers for a cubic system of differential equations. Zbl 1416.34020Algaba, Antonio; García, Cristóbal; Giné, Jaume 7 2019 Integrability of planar nilpotent differential systems through the existence of an inverse integrating factor. Zbl 1464.34006Algaba, Antonio; García, Cristóbal; Giné, Jaume 5 2019 Study of a dynamical system with a strange attractor and invariant tori. Zbl 1470.37084Algaba, Antonio; Merino, Manuel; Qin, Bo-Wei; Rodríguez-Luis, Alejandro J. 1 2019 The center problem for \(\mathbb{Z}_2\)-symmetric nilpotent vector fields. Zbl 1395.34047Algaba, Antonio; García, Cristóbal; Giné, Jaume; Llibre, Jaume 12 2018 Analytical integrability problem for perturbations of cubic Kolmogorov systems. Zbl 1404.37021Algaba, Antonio; García, Cristóbal; Reyes, Manuel 6 2018 Nondegenerate centers and limit cycles of cubic Kolmogorov systems. Zbl 1390.37082Algaba, Antonio; García, Cristóbal; Giné, Jaume 3 2018 Structural stability of planar quasi-homogeneous vector fields. Zbl 1405.34047Algaba, A.; Fuentes, N.; Gamero, E.; Garcia, C. 2 2018 A bifurcation analysis of planar nilpotent reversible systems. Zbl 1372.34073Algaba, A.; Freire, E.; Gamero, E.; García, C. 4 2017 Nilpotent centres via inverse integrating factors. Zbl 1384.34037Algaba, Antonio; García, Cristóbal; Giné, Jaume 10 2016 The center problem. A view from the normal form theory. Zbl 1329.34071Algaba, A.; Gamero, E.; García, C. 9 2016 Geometric criterium in the center problem. Zbl 1356.34035Algaba, Antonio; García, Cristóbal; Giné, Jaume 6 2016 Analytic integrability inside a family of degenerate centers. Zbl 1354.34005Algaba, Antonio; Checa, Isabel; García, Cristóbal; Giné, Jaume 5 2016 Superluminal periodic orbits in the Lorenz system. Zbl 1510.34082Algaba, A.; Merino, M.; Rodríguez-Luis, A. J. 3 2016 Analytic integrability of some examples of degenerate planar vector fields. Zbl 1343.34003Algaba, Antonio; García, Cristóbal; Giné, Jaume 2 2016 On orbital-reversibility for a class of planar dynamical systems. Zbl 1337.34039Algaba, A.; Checa, I.; García, C.; Gamero, E. 12 2015 An exact homoclinic orbit and its connection with the Rössler system. Zbl 1396.37027Algaba, A.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 8 2015 Takens-Bogdanov bifurcations of equilibria and periodic orbits in the Lorenz system. Zbl 1489.37069Algaba, A.; Domínguez-Moreno, M. C.; Merino, M.; Rodríguez-Luis, A. J. 8 2015 Study of the Hopf bifurcation in the Lorenz, Chen and Lü systems. Zbl 1345.34069Algaba, Antonio; Domínguez-Moreno, María C.; Merino, Manuel; Rodríguez-Luis, Alejandro J. 7 2015 Analysis of the T-point-Hopf bifurcation in the Lorenz system. Zbl 1329.37082Algaba, A.; Fernández-Sánchez, F.; Merino, M.; Rodríguez-Luis, A. J. 7 2015 Monodromy of a class of analytic generalized nilpotent systems through their Newton diagram. Zbl 1322.34049Algaba, A.; García, C.; Reyes, M. 1 2015 Comments on: “Invariant algebraic surfaces of the generalized Lorenz system”. Zbl 1323.34019Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 1 2015 Analytic integrability for some degenerate planar vector fields. Zbl 1306.34046Algaba, Antonio; García, Cristóbal; Giné, Jaume 11 2014 Centers on center manifolds in the Lorenz, Chen and Lü systems. Zbl 1457.34061Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 9 2014 A class of non-integrable systems admitting an inverse integrating factor. Zbl 1333.37076Algaba, A.; Fuentes, N.; García, C.; Reyes, M. 9 2014 On Darboux polynomials and rational first integrals of the generalized Lorenz system. Zbl 1302.34001Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 7 2014 A new algorithm for determining the monodromy of a planar differential system. Zbl 1334.34188Algaba, A.; García, C.; Reyes, M. 6 2014 Comments on “Global dynamics of the generalized Lorenz systems having invariant algebraic surfaces”. Zbl 1291.34080Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 5 2014 Comments on “The Chen system revisited”. Zbl 1306.34020Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 4 2014 Comment on “A constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family”. Zbl 1470.37040Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 2 2014 Comments on “Dynamics of the general Lorenz family” by Y. Liu and W. Pang. Zbl 1319.37011Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 2 2014 Comment on “Existence of heteroclinic and homoclinic orbits in two different chaotic dynamical systems”. Zbl 1335.37011Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 1 2014 Chen’s attractor exists if Lorenz repulsor exists: The Chen system is a special case of the Lorenz system. Zbl 1323.37020Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 30 2013 The Lü system is a particular case of the Lorenz system. Zbl 1301.37020Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 22 2013 On the formal integrability problem for planar differential systems. Zbl 1282.34005Algaba, Antonio; García, Cristóbal; Giné, Jaume 6 2013 Analytic integrability for some degenerate planar systems. Zbl 1278.34001Algaba, Antonio; García, Cristóbal; Giné, Jaume 5 2013 Comment on ‘Šilnikov-type orbits of Lorenz-family systems’. Zbl 1395.37020Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 5 2013 The reversibility problem for quasi-homogeneous dynamical systems. Zbl 1283.34032Algaba, Antonio; Gamero, Estanislao; García, Cristóbal 2 2013 Comments on “Non-existence of Shilnikov chaos in continuous-time systems”. Zbl 1277.65108Algaba, A.; Fernández-Sánchez, F.; Merino, M.; Rodríguez-Luis, A. J. 2 2013 Centers of quasi-homogeneous polynomial planar systems. Zbl 1238.34052Algaba, A.; Fuentes, N.; García, C. 28 2012 Existence of an inverse integrating factor, center problem and integrability of a class of nilpotent systems. Zbl 1266.37023Algaba, A.; García, C.; Reyes, M. 22 2012 Analysis of a Belyakov homoclinic connection with \(\mathbb Z_2\)-symmetry. Zbl 1268.37017Algaba, Antonio; Merino, Manuel; Rodríguez-Luis, Alejandro J. 6 2012 Comment on “Existence of heteroclinic orbits of the Shil’nikov type in a 3D quadratic autonomous chaotic system”. Zbl 1247.34072Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 4 2012 A note on analytic integrability of planar vector fields. Zbl 1268.34003Algaba, A.; García, C.; Reyes, M. 4 2012 Homoclinic interactions near a triple-zero degeneracy in Chua’s equation. Zbl 1270.34113Algaba, Antonio; Merino, Manuel; Rodríguez-Luis, Alejandro J. 3 2012 Integrability of two dimensional quasi-homogeneous polynomial differential systems. Zbl 1213.37093Algaba, A.; García, C.; Reyes, M. 24 2011 Characterization of a monodromic singular point of a planar vector field. Zbl 1226.34031Algaba, A.; García, C.; Reyes, M. 13 2011 Comment on “Sil’nikov chaos of the Liu system”. Zbl 1317.34083Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 7 2011 Nilpotent systems admitting an algebraic inverse integrating factor over \(\mathbb{C}((x,y))\). Zbl 1267.34002Algaba, Antonio; García, Cristóbal; Reyes, Manuel 6 2011 Hopf bifurcations and their degeneracies in Chua’s equation. Zbl 1248.34059Algaba, Antonio; Merino, Manuel; Fernández-Sánchez, Fernando; Rodríguez-Luis, Alejandro J. 4 2011 Monodromy, center-focus and integrability problems for quasi-homogeneous polynomial systems. Zbl 1192.34035Algaba, A.; Freire, E.; Gamero, E.; García, C. 16 2010 Reversibility and quasi-homogeneous normal forms of vector fields. Zbl 1202.34069Algaba, A.; García, C.; Teixeira, M. A. 12 2010 Rational integrability of two-dimensional quasi-homogeneous polynomial differential systems. Zbl 1201.34050Algaba, A.; García, C.; Reyes, M. 10 2010 Analysis of the T-point-Hopf bifurcation with \(\mathbb Z_2\)-symmetry. Application to Chua’s equation. Zbl 1193.34078Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J. 3 2010 The integrability problem for a class of planar systems. Zbl 1165.34023Algaba, A.; Gamero, E.; García, C. 58 2009 Like-linearizations of vector fields. Zbl 1196.37080Algaba, A.; García, C.; Reyes, M. 11 2009 Characterizing isochronous points and computing isochronous sections. Zbl 1208.34034Algaba, A.; Reyes, M. 11 2009 Local bifurcation of limit cycles and integrability of a class of nilpotent systems of differential equations. Zbl 1201.34061Algaba, A.; García, C.; Reyes, M. 10 2009 Degenerate global bifurcations in a simple circuit. Zbl 1187.37072Algaba, A.; Merino, M.; García, C.; Reyes, M. 1 2009 The center problem for a family of systems of differential equations having a nilpotent singular point. Zbl 1156.34031Algaba, A.; García, C.; Reyes, M. 25 2008 Isochronous centres and foci via commutators and normal forms. Zbl 1155.34018Algaba, A.; Reyes, M. 6 2008 Resonances of periodic orbits in Rössler system in presence of a triple-zero bifurcation. Zbl 1145.37322Algaba, Antonio; Freire, Emilio; Gamero, Estanislao; Rodríguez-Luis, Alejandro J. 9 2007 A degenerate Hopf-saddle-node bifurcation analysis in a family of electronic circuits. Zbl 1201.37021Algaba, A.; Gamero, E.; García, C.; Merino, M. 6 2007 Open-to-closed curves of saddle-node bifurcations of periodic orbits near a nontransversal T-point in Chua’s equation. Zbl 1142.34029Algaba, Antonio; Merino, Manuel; Fernández-Sánchez, Fernando; Rodríguez-Luis, Alejandro J. 5 2006 A bifurcation analysis of a simple electronic circuit. Zbl 1064.34030Algaba, A.; Gamero, E.; Rodríguez-Luis, A. J. 11 2005 Homoclinic connections near a Belyakov point in Chua’s equation. Zbl 1089.37019Algaba, A.; Merino, M.; Rodríguez-Luis, A. J. 4 2005 An algorithm for computing quasi-homogeneous formal normal forms under equivalence. Zbl 1063.34029Algaba, Antonio; Freire, Emilio; Gamero, Estanislao; García, Cristóbal 13 2004 Quasi-homogeneous normal forms. Zbl 1022.34034Algaba, A.; Freire, E.; Gamero, E.; García, C. 28 2003 Some results on Chua’s equation near a triple-zero linear degeneracy. Zbl 1083.93020Algaba, A.; Merino, M.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 21 2003 Computing center conditions for vector fields with constant angular speed. Zbl 1032.34026Algaba, A.; Reyes, M. 17 2003 Closed curves of global bifurcations in Chua’s equation: a mechanism for their formation. Zbl 1056.37067Algaba, Antonio; Merino, Manuel; Fernández-Sánchez, Fernando; Rodríguez-Luis, Alejandro J. 7 2003 Centers with degenerate infinity and their commutators. Zbl 1037.34024Algaba, A.; Reyes, M. 6 2003 Quasi-homogeneous normal forms for null linear part. Zbl 1054.34065Algaba, A.; Freire, E.; Gamero, E.; García, C. 2 2003 A note on the triple-zero linear degeneracy: normal forms, dynamical and bifurcation behaviors of an unfolding. Zbl 1043.37042Freire, E.; Gamero, E.; Rodríguez-Luis, A. J.; Algaba, A. 34 2002 Nontransversal curves of \(T\)-points: A source of closed curves of global bifurcations. Zbl 0999.37035Algaba, A.; Fernández-Sánchez, F.; Freire, E.; Merino, M.; Rodríguez-Luis, A. J. 11 2002 Computing simplest normal forms for the Takens-Bogdanov singularity. Zbl 1050.34052Algaba, Antonio 6 2002 Oscillation-sliding in a modified van der Pol-Duffing electronic oscillator. Zbl 1237.34049Algaba, A.; Fernández-Sánchez, F.; Freire, E.; Gamero, E.; Rodríguez-Luis, A. J. 4 2002 Geometry of the uniformly isochronous centers with polynomial commutator. Zbl 1231.34052Algaba, A.; Reyes, M.; Bravo, A. 4 2002 Takens-Bogdanov bifurcations of periodic orbits and Arnold’s tongues in a three-dimensional electronic model. Zbl 1090.37543Algaba, A.; Merino, M.; Rodríguez-Luis, A. J. 9 2001 Characterizing and computing normal forms using Lie transforms: A survey. Zbl 1001.34030Algaba, A.; Freire, E.; Gamero, E. 8 2001 ...and 10 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 433 Authors 99 Algaba, Antonio 51 Rodríguez-Luis, Alejandro J. 49 García, Cristóbal 38 Giné, Jaume 29 Merino, Manuel 27 Llibre, Jaume 26 Reyes, Manuel 25 Fernández-Sánchez, Fernando 24 Freire Macías, Emilio 19 Gamero, Estanislao 17 Yu, Pei 14 García, Isaac A. 13 Qin, Bo-Wei 12 Chung, Kwok-Wai 11 Valls Anglés, Cláudia 10 Gazor, Majid 9 Li, Feng 7 Fuentes, Natalia 6 Maza, Susanna 6 Sabatini, Marco 5 Amel’kin, Vladimir Vasilievich 5 Barrio, Roberto 5 Carmona, Victoriano 5 Liang, Haihua 5 Liu, Xingbo 5 Liu, Yirong 5 Ponce, Enrique 5 Torregrosa, Joan 5 Zhang, Fuchen 4 Checa, Isabel 4 Edneral, Victor F. 4 Ferčec, Brigita 4 Han, Maoan 4 Ibáñez, Santiago 4 Itikawa, Jackson 4 Li, Chunbiao 4 Shoghi, Ahmad 4 Sprott, Julien Clinton 4 Teruel, Antonio E. 4 Wang, Duo 3 Bella, Giovanni 3 Bi, Qinsheng 3 Domínguez-Moreno, María C. 3 Drubi, Fátima 3 Fernández-García, Soledad 3 García-Medina, Elisabeth 3 Gasull, Armengol 3 Grau, Maite 3 Guo, Shangjiang 3 Kapitaniak, Tomasz 3 Krauskopf, Bernd 3 Li, Jing 3 Liao, Xiaofeng 3 Liu, Xia 3 Mokhtari, Fahimeh 3 Oliveira, Regilene D. S. 3 Pessoa, Claudio 3 Rocha, Ronilson 3 Romanovskiĭ, Valeriĭ Georgievich 3 Sánchez-Sánchez, Iván 3 Serrano, Sergio E. 3 Shafer, Douglas S. 3 Tang, Yilei 3 Teixeira, Marco Antonio 3 Tian, Yuzhou 3 Wu, Yusen 3 Yang, Shuangling 3 Yuan, Yuan 3 Zhang, Guangyun 3 Zhou, Zhengxin 2 Alonso, Diego M. 2 Belhaq, Mohamed 2 Blesa, Fernando 2 Bruno, Alexander Dmitrievich 2 Buică, Adriana 2 Chen, Guanrong 2 Chen, Haibo 2 Dukarić, Maša 2 Esteban, Marina 2 García-Saldaña, Johanna D. 2 Guillamon, Antoni 2 Guo, Lina 2 Horikawa, Yo 2 Huang, Jianfeng 2 Huang, Wentao 2 Jiang, Jiao 2 Kitajima, Hiroyuki 2 Kou, Liying 2 Lamb, Jeroen S. W. 2 Leung, Andrew Yee-Tak 2 Li, Shimin 2 Liu, Xuanliang 2 Liu, Yuanyuan 2 Mahdi, Adam 2 Makhlouf, Amar 2 Marwan, Muhammad 2 Mattana, Paolo 2 Medrano-T, Rene Orlando 2 Moiola, Jorge Luis 2 Mu, Chunlai ...and 333 more Authors all top 5 Cited in 84 Serials 72 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 32 Journal of Differential Equations 23 Journal of Mathematical Analysis and Applications 18 Chaos, Solitons and Fractals 18 Qualitative Theory of Dynamical Systems 17 Nonlinear Dynamics 15 Physica D 13 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 13 Communications in Nonlinear Science and Numerical Simulation 12 Applied Mathematics and Computation 11 Chaos 10 Nonlinear Analysis. Real World Applications 7 Journal of Computational and Applied Mathematics 6 Physics Letters. 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Series B 1 Revista Matemática Iberoamericana 1 Dynamics and Stability of Systems 1 Neural Computation 1 Economics Letters 1 Journal of Mathematical Sciences (New York) 1 Electronic Journal of Differential Equations (EJDE) 1 Computational and Applied Mathematics 1 Journal of Mathematical Chemistry 1 Soft Computing 1 Discrete Dynamics in Nature and Society 1 New Journal of Physics 1 Journal of Nonlinear Mathematical Physics 1 Nonlinear Analysis. Modelling and Control 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms 1 Journal of Systems Science and Complexity 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Communications on Pure and Applied Analysis 1 Journal of Dynamical Systems and Geometric Theories 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Journal of Statistical Mechanics: Theory and Experiment 1 Mathematical Biosciences and Engineering 1 Advances in Mathematical Physics 1 Advances in Nonlinear Analysis 1 Journal of Mathematics 1 European Journal of Mathematics 1 International Journal of Applied and Computational Mathematics 1 Bollettino dell’Unione Matematica Italiana all top 5 Cited in 29 Fields 340 Ordinary differential equations (34-XX) 168 Dynamical systems and ergodic theory (37-XX) 24 Biology and other natural sciences (92-XX) 20 Mechanics of particles and systems (70-XX) 17 Numerical analysis (65-XX) 13 Information and communication theory, circuits (94-XX) 12 Systems theory; control (93-XX) 9 Computer science (68-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Optics, electromagnetic theory (78-XX) 3 Nonassociative rings and algebras (17-XX) 3 Fluid mechanics (76-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Partial differential equations (35-XX) 2 Operator theory (47-XX) 1 General and overarching topics; collections (00-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year