Regular and Chaotic DynamicsInternational Scientific Journal Short Title: Regul. Chaotic Dyn. Publisher: Springer US, New York, NY; Pleiades Publishing, New York, NY; MAIK “Nauka/Interperiodica”, Moscow ISSN: 1560-3547; 1468-4845/e Online: http://link.springer.com/journal/volumesAndIssues/11819http://www.turpion.org/php/homes/pa.phtml?jrnid=rdhttp://ics.org.ru/journals/rcd/ Predecessor: Regularnaya & Khaoticheskaya Dinamika Comments: Indexed cover-to-cover Documents Indexed: 1,113 Publications (since 1998) References Indexed: 767 Publications with 21,414 References. all top 5 Latest Issues 27, No. 6 (2022) 27, No. 5 (2022) 27, No. 4 (2022) 27, No. 3 (2022) 27, No. 2 (2022) 27, No. 1 (2022) 26, No. 6 (2021) 26, No. 5 (2021) 26, No. 4 (2021) 26, No. 3 (2021) 26, No. 2 (2021) 26, No. 1 (2021) 25, No. 6 (2020) 25, No. 5 (2020) 25, No. 4 (2020) 25, No. 3 (2020) 25, No. 2 (2020) 25, No. 1 (2020) 24, No. 6 (2019) 24, No. 5 (2019) 24, No. 4 (2019) 24, No. 3 (2019) 24, No. 2 (2019) 24, No. 1 (2019) 23, No. 7-8 (2018) 23, No. 6 (2018) 23, No. 5 (2018) 23, No. 4 (2018) 23, No. 3 (2018) 23, No. 2 (2018) 23, No. 1 (2018) 22, No. 8 (2017) 22, No. 7 (2017) 22, No. 6 (2017) 22, No. 5 (2017) 22, No. 4 (2017) 22, No. 3 (2017) 22, No. 2 (2017) 22, No. 1 (2017) 21, No. 7-8 (2016) 21, No. 6 (2016) 21, No. 5 (2016) 21, No. 4 (2016) 21, No. 3 (2016) 21, No. 2 (2016) 21, No. 1 (2016) 20, No. 6 (2015) 20, No. 5 (2015) 20, No. 4 (2015) 20, No. 3 (2015) 20, No. 2 (2015) 20, No. 1 (2015) 19, No. 6 (2014) 19, No. 5 (2014) 19, No. 4 (2014) 19, No. 3 (2014) 19, No. 2 (2014) 19, No. 1 (2014) 18, No. 6 (2013) 18, No. 5 (2013) 18, No. 4 (2013) 18, No. 3 (2013) 18, No. 1-2 (2013) 17, No. 6 (2012) 17, No. 5 (2012) 17, No. 3-4 (2012) 17, No. 2 (2012) 17, No. 1 (2012) 16, No. 6 (2011) 16, No. 5 (2011) 16, No. 3-4 (2011) 16, No. 1-2 (2011) 15, No. 6 (2010) 15, No. 4-5 (2010) 15, No. 2-3 (2010) 15, No. 1 (2010) 14, No. 6 (2009) 14, No. 4-5 (2009) 14, No. 3 (2009) 14, No. 2 (2009) 14, No. 1 (2009) 13, No. 6 (2008) 13, No. 5 (2008) 13, No. 4 (2008) 13, No. 3 (2008) 13, No. 2 (2008) 13, No. 1 (2008) 12, No. 6 (2007) 12, No. 5 (2007) 12, No. 4 (2007) 12, No. 3 (2007) 12, No. 2 (2007) 12, No. 1 (2007) 11, No. 4 (2006) 11, No. 3 (2006) 11, No. 2 (2006) 11, No. 1 (2006) 10, No. 4 (2005) 10, No. 3 (2005) 10, No. 2 (2005) ...and 27 more Volumes all top 5 Authors 95 Borisov, Alekseĭ Vladimirovich 83 Mamaev, Ivan Sergeevich 42 Kilin, Aleksandr Aleksandrovich 30 Tsyganov, Andreĭ Vladimirovich 28 Kozlov, Valeriĭ Vasil’evich 25 Kudryashov, Nikolaĭ Alekseevich 21 Bizyaev, Ivan Alekseevich 18 Kuznetsov, Sergey P. 17 Wiggins, Stephen 16 Gonchenko, Sergey V. 15 Dragović, Vladimir 13 Markeev, Anatoliĭ Pavlovich 12 Bardin, Boris Sabirovich 11 Ivanov, Aleksandr Pavlovich 11 Morozov, Al’bert Dmitrievich 11 Przybylska, Maria 10 Grammaticos, Basil 10 Turaev, Dmitry V. 9 Bolotin, Sergeĭ Vladimirovich 9 Neĭshtadt, Anatoliĭ Iserovich 9 Simó, Carles 9 Treshchev, Dmitriĭ Valer’evich 9 Vidal, Claudio 8 Carton, Xavier J. 8 Kazakov, Alexey O. 8 Pivovarova, Elena Nikolaevna 8 Sevryuk, Mikhail Borisovich 8 Vetchanin, Evgeniĭ Vladimirovich 7 Albouy, Alain 7 Bolsinov, Alexey V. 7 Cushman, Richard H. 7 Dullin, Holger R. 7 Fassò, Francesco 7 Gajić, Borislav 7 Kharlamov, Mikhail Pavlovich 7 Kurakin, Leonid Gennadievich 7 Lerman, Lev 7 Maciejewski, Andrzej J. 7 O’Neil, Kevin Anthony 7 Pochinka, Olga Vital’evna 7 Ramani, Alfred 7 Rauch-Wojciechowski, Stefan 7 Sokolovskiy, Mikhail A. 6 Anishchenko, Vadim Semenovich 6 Broer, Henk W. 6 Cabral, Hildeberto Eulalio 6 Chaplygin, Sergeĭ Alekseevich 6 Chenciner, Alain 6 Damianou, Pantelis Andrea 6 Grines, Vyacheslav Zigmundovich 6 Osipov, Grigory V. 6 Ryabov, Pavel Evgen’evich 6 Yehia, Hamad M. 5 Celletti, Alessandra 5 Chierchia, Luigi 5 Demina, Maria V. 5 Fedorov, Yuri N. 5 Karavaev, Yurĭ Leonidovich 5 Koiller, Jair 5 Radnović, Milena 5 Sataev, Igor’ Rustamovich 5 Shafarevich, Andreĭ Igorevich 5 Stremler, Mark A. 4 Artemova, Elizaveta Markovna 4 Biswas, Anjan 4 Bogoyavlenskij, Oleg Igorevich 4 Bounemoura, Abed Bounemoura 4 Burov, Aleksandr Anatol’evich 4 Chekina, Evgeniya Alekseevna 4 Delshams, Amadeu 4 Dritschel, David Gerard 4 Elipe, Antonio 4 Gal’perin, G. A. 4 García-Naranjo, Luis C. 4 Gelfreich, Vassili 4 Gonchenko, Marina S. 4 Guzzo, Massimiliano 4 Hanßmann, Heinz 4 Holmes, Philip J. 4 Inozemtsev, Vladimir I. 4 Jovanović, Božidar Žarko 4 Koudjinan, Comlan E. 4 Lanchares, Víctor 4 Meiss, James D. 4 Meyer, Kenneth R. 4 Miranda, Eva 4 Negrini, Piero 4 Novokshenov, Viktor Yur’evich 4 Ostrovskaya, Irina V. 4 Ovsyannikov, Ivan I. 4 Pedroni, Marco 4 Polekhin, Ivan Yu. 4 Ramodanov, Sergey M. 4 Reinaud, Jean N. 4 Rudnev, Misha 4 Sachkov, Yuriĭ Leonidovich 4 Sansonetto, Nicola 4 Shilnikov, Andrey L. 4 Sinaĭ, Yakov Grigor’evich 4 Sinelshchikov, Dmitry I. ...and 898 more Authors all top 5 Fields 719 Dynamical systems and ergodic theory (37-XX) 582 Mechanics of particles and systems (70-XX) 191 Ordinary differential equations (34-XX) 133 Fluid mechanics (76-XX) 83 Differential geometry (53-XX) 54 Partial differential equations (35-XX) 41 History and biography (01-XX) 30 Statistical mechanics, structure of matter (82-XX) 26 Biology and other natural sciences (92-XX) 25 Global analysis, analysis on manifolds (58-XX) 24 Quantum theory (81-XX) 23 Mechanics of deformable solids (74-XX) 21 Algebraic geometry (14-XX) 21 Numerical analysis (65-XX) 20 Systems theory; control (93-XX) 18 Difference and functional equations (39-XX) 14 Special functions (33-XX) 14 Optics, electromagnetic theory (78-XX) 13 Calculus of variations and optimal control; optimization (49-XX) 11 Geophysics (86-XX) 10 Topological groups, Lie groups (22-XX) 10 Manifolds and cell complexes (57-XX) 8 Number theory (11-XX) 8 Measure and integration (28-XX) 8 Probability theory and stochastic processes (60-XX) 7 General and overarching topics; collections (00-XX) 7 Operator theory (47-XX) 6 Nonassociative rings and algebras (17-XX) 6 Computer science (68-XX) 6 Relativity and gravitational theory (83-XX) 5 Combinatorics (05-XX) 5 Functions of a complex variable (30-XX) 5 Convex and discrete geometry (52-XX) 5 General topology (54-XX) 4 Real functions (26-XX) 4 Several complex variables and analytic spaces (32-XX) 3 Commutative algebra (13-XX) 3 Approximations and expansions (41-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Field theory and polynomials (12-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Potential theory (31-XX) 2 Integral equations (45-XX) 2 Algebraic topology (55-XX) 2 Operations research, mathematical programming (90-XX) 1 Sequences, series, summability (40-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Geometry (51-XX) 1 Astronomy and astrophysics (85-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 841 Publications have been cited 5,711 times in 2,955 Documents Cited by ▼ Year ▼ Invariant tori in non-degenerate nearly integrable Hamiltonian systems. Zbl 0992.37050Rüssmann, H. 94 2001 Rolling of a rigid body on a plane and sphere. Hierarchy of dynamics. Zbl 1058.70009Borisov, A. V.; Mamaev, I. S. 68 2002 Conservation laws, hierarchy of dynamics and explicit integration of nonholonomic systems. Zbl 1229.70038Borisov, A. V.; Mamaev, I. S. 66 2008 On the theory of motion of nonholonomic systems. The reducing-multiplier theorem. Translated from the Russian 1911 original. Zbl 1229.37082Chaplygin, S. A. 61 2008 Rolling of a ball on a surface. New integrals and hierarchy of dynamics. Zbl 1058.70010Borisov, A. V.; Mamaev, I. S.; Kilin, A. A. 59 2002 The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere. Zbl 1367.70007Borisov, Alexey V.; Mamaev, Ivan S.; Bizyaev, Ivan A. 55 2013 Richness of chaotic dynamics in nonholonomic models of a Celtic stone. Zbl 1417.37222Gonchenko, Alexander S.; Gonchenko, Sergey V.; Kazakov, Alexey O. 52 2013 How to control Chaplygin’s sphere using rotors. Zbl 1264.37016Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 49 2012 On a ball’s rolling on a horizontal plane. Translated from the Russian 1903 original. Zbl 1058.70003Chaplygin, S. A. 45 2002 Invariant curves of analytic perturbed nontwist area preserving maps. Zbl 0932.37048Simó, C. 45 1998 Trajectory equivalence and corresponding integrals. Zbl 0928.37003Matveev, V. S.; Topalov, P. Ĭ. 41 1998 How to control the Chaplygin ball using rotors. II. Zbl 1303.37021Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 39 2013 The problem of drift and recurrence for the rolling Chaplygin ball. Zbl 1286.70007Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 37 2013 Dynamical phenomena occurring due to phase volume compression in nonholonomic model of the rattleback. Zbl 1263.74021Borisov, Alexey V.; Jalnine, Alexey Yu.; Kuznetsov, Sergey P.; Sataev, Igor R.; Sedova, Julia V. 36 2012 The reversal and chaotic attractor in the nonholonomic model of Chaplygin’s top. Zbl 1358.70006Borisov, Alexey V.; Kazakov, Alexey O.; Sataev, Igor R. 35 2014 Two-body problem on a sphere. Reduction, stochasticity, periodic orbits. Zbl 1065.37058Borisov, A. V.; Mamaev, I. S.; Kilin, A. A. 33 2004 On the integration theory of equations of nonholonomic mechanics. Zbl 1006.37040Kozlov, V. V. 33 2002 Symmetries and reduction in nonholonomic mechanics. Zbl 1342.37001Borisov, Alexey V.; Mamaev, Ivan S. 31 2015 Hamiltonization of non-holonomic systems in the neighborhood of invariant manifolds. Zbl 1309.37049Bolsinov, A. V.; Borisov, A. V.; Mamaev, I. S. 31 2011 Chaplygin ball over a fixed sphere: an explicit integration. Zbl 1229.37080Borisov, A. V.; Fedorov, Yu. N.; Mamaev, I. S. 31 2008 The dynamics of Chaplygin ball: the qualitative and computer analysis. Zbl 1074.70513Kilin, A. A. 31 2001 The Jacobi integral in nonholonomic mechanics. Zbl 1367.70036Borisov, Alexey V.; Mamaev, Ivan. S.; Bizyaev, Ivan. A. 30 2015 Popular ansatz methods and solitary wave solutions of the Kuramoto-Sivashinsky equation. Zbl 1229.34008Kudryashov, N. A.; Soukharev, M. B. 30 2009 Chaotic dynamics of three-dimensional Hénon maps that originate from a homoclinic bifurcation. Zbl 1164.37306Gonchenko, S. V.; Meiss, J. D.; Ovsyannikov, I. I. 28 2006 The dynamics and control of a spherical robot with an internal omniwheel platform. Zbl 1317.93192Karavaev, Yury L.; Kilin, Alexander A. 28 2015 Quasi-periodic bifurcations of invariant circles in low-dimensional dissipative dynamical systems. Zbl 1225.37087Vitolo, Renato; Broer, Henk; Simó, Carles 27 2011 Asymptotic stability and associated problems of dynamics of falling rigid body. Zbl 1229.37107Borisov, A. V.; Kozlov, V. V.; Mamaev, I. S. 27 2007 Strange attractors and mixed dynamics in the problem of an unbalanced rubber ball rolling on a plane. Zbl 1417.37223Kazakov, Alexey O. 27 2013 On a paper of Moeckel on central configurations. Zbl 1061.70006Albouy, A. 27 2003 On integrability of Hirota-Kimura type discretizations. Zbl 1258.37067Petrera, Matteo; Pfadler, Andreas; Suris, Yuri B. 26 2011 Bifurcations of Liouville tori in elliptical billiards. Zbl 1229.37065Dragović, V.; Radnović, M. 26 2009 Rubber rolling over a sphere. Zbl 1229.37089Koiller, Jair; Ehlers, Kurt 25 2007 Billiard dynamics: a survey with the emphasis on open problems. Zbl 1023.37022Gutkin, E. 25 2003 Hamiltonicity and integrability of the Suslov problem. Zbl 1277.70008Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 24 2011 The dynamics of nonholonomic systems consisting of a spherical shell with a moving rigid body inside. Zbl 1308.70003Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 24 2014 Solitary and periodic solutions of the generalized Kuramoto-Sivashinsky equation. Zbl 1229.35229Kudryashov, N. A. 24 2008 The Chaplygin sleigh with parametric excitation: chaotic dynamics and nonholonomic acceleration. Zbl 1398.37056Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 23 2017 Mock (false) theta functions as quantum invariants. Zbl 1133.57301Hikami, K. 23 2005 Spherical robot of combined type: dynamics and control. Zbl 1339.93081Kilin, Alexander A.; Pivovarova, Elena N.; Ivanova, Tatyana B. 22 2015 Dynamics and statics of vortices on a plane and a sphere. I. Zbl 0934.76014Borisov, A. V.; Pavlov, A. E. 22 1998 On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors. Zbl 1229.37041Gonchenko, S. V.; Shilnikov, L. P.; Turaev, D. V. 22 2009 The role of normally hyperbolic invariant manifolds (NHIMS) in the context of the phase space setting for chemical reaction dynamics. Zbl 1369.34068Wiggins, Stephen 22 2016 Dynamics of rolling disk. Zbl 1112.37320Borisov, A. V.; Mamaev, I. S.; Kilin, A. A. 22 2003 KAM à la R. Zbl 1219.37044Pöschel, Jürgen 21 2011 Bi-Hamiltonian structures and singularities of integrable systems. Zbl 1229.37092Bolsinov, A. V.; Oshemkov, A. A. 21 2009 Topological analysis of an integrable system related to the rolling of a ball on a sphere. Zbl 1334.37059Borisov, Alexey V.; Mamaev, Ivan S. 21 2013 Simultaneous separation for the Neumann and Chaplygin systems. Zbl 1325.37052Tsiganov, Andrey 21 2015 Rolling of a ball without spinning on a plane: the absence of an invariant measure in a system with a complete set of integrals. Zbl 1267.37066Bolsinov, Alexey V.; Borisov, Alexey V.; Mamaev, Ivan S. 21 2012 Higher dimensional continued fractions. Zbl 1044.11596Arnold, V. I. 21 1998 Nekhoroshev-stability of \(L4\) and \(L5\) in the spatial restricted three-body problem. Zbl 0934.70010Benettin, G.; Fassò, F.; Guzzo, M. 21 1998 Rolling of a non-homogeneous ball over a sphere without slipping and twisting. Zbl 1229.37081Borisov, A. V.; Mamaev, I. S. 20 2007 On a motion of a heavy body of revolution on a horizontal plane. Translated from the Russian 1897 original. Zbl 1058.70002Chaplygin, S. A. 20 2002 Poisson brackets for the dynamically interacting system of a 2D rigid cylinder and \(N\) point vortices: the case of arbitrary smooth cylinder shapes. Zbl 1128.76315Shashikanth, B. N. 19 2005 Generalized Chaplygin’s transformation and explicit integration of a system with a spherical support. Zbl 1253.37063Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 19 2012 Bifurcations of three-dimensional diffeomorphisms with non-simple quadratic homoclinic tangencies and generalized Hénon maps. Zbl 1229.37040Gonchenko, S. V.; Gonchenko, V. S.; Tatjer, J. C. 19 2007 An integrability of the problem on motion of cylinder and vortex in the ideal fluid. Zbl 1112.37315Borisov, A. V.; Mamaev, I. S. 19 2003 Motion of a circular cylinder and \(n\) point vortices in a perfect fluid. Zbl 1051.76009Borisov, A. V.; Mamaev, I. S.; Ramodanov, S. M. 19 2003 Total collison, completely parabolic motions and homothety reduction in the \(n\)-body problem. (Collisions totales, mouvements complètement paraboliques et réduction des homothéties dans le problème des \(n\) corps.) Zbl 0973.70011Chenciner, A. 19 1998 Geometric integration via multi-space. Zbl 1068.65092Kim, Pilwon; Olver, Peter J. 18 2004 Two variations on the theme of Lamb–Chaplygin: supersmooth dipole and rotating multipoles. Zbl 1102.76008Kizner, Ziv; Khvoles, R. 18 2004 On the Hadamard-Hamel problem and the dynamics of wheeled vehicles. Zbl 1367.70034Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 18 2015 The spatial problem of 2 bodies on a sphere. Reduction and stochasticity. Zbl 1402.70015Borisov, Alexey V.; Mamaev, Ivan S.; Bizyaev, Ivan A. 18 2016 Stability of Thomson’s configurations of vortices on a sphere. Zbl 0967.76023Borisov, A. V.; Kilin, A. A. 18 2000 On the dynamic model and motion planning for a spherical rolling robot actuated by orthogonal internal rotors. Zbl 1272.70049Svinin, Mikhail; Morinaga, Akihiro; Yamamoto, Motoji 17 2013 The dynamics of orbits in a potential field of a solid circular ring. Zbl 1128.70308Broucke, R. A.; Elipe, A. 17 2005 Periodic flows, rank-two Poisson structures, and nonholonomic mechanics. Zbl 1077.37043Fassò, F.; Giacobbe, A.; Sansonetto, N. 17 2005 Dynamics of heton-like vortices. Zbl 1164.76423Gryanik, V. M.; Sokolovskiy, M. A.; Verron, J. 17 2006 Higher Painlevé transcendents as special solutions of some nonlinear integrable hierarchies. Zbl 1328.35193Kudryashov, Nikolay A. 17 2014 Dynamics of the Suslov problem in a gravitational field: reversal and strange attractors. Zbl 1344.37073Bizyaev, Ivan A.; Borisov, Alexey V.; Kazakov, Alexey O. 17 2015 Multiparticle systems. The algebra of integrals and integrable cases. Zbl 1229.37106Borisov, A. V.; Kilin, A. A.; Mamaev, I. S. 17 2009 The type numbers of closed geodesics. Zbl 1229.58015Taimanov, I. A. 17 2010 Synchronization of Chimera states in a network of many unidirectionally coupled layers of discrete maps. Zbl 1411.90070Strelkova, Galina I.; Vadivasova, Tatiana E.; Anishchenko, Vadim S. 16 2018 Exotic dynamics of nonholonomic roller racer with periodic control. Zbl 1412.37064Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 16 2018 Asymmetric discrete Painlevé equations. Zbl 0983.34083Kruskal, M. D.; Tamizhmani, K. M.; Grammaticos, B.; Ramani, A. 16 2000 Absolute and relative choreographies in the problem of point vortices moving on a plane. Zbl 1079.76020Borisov, A. V.; Mamaev, I. S.; Kilin, A. A. 15 2004 Dynamics of three vortices on a plane and a sphere. II: General compact case. Zbl 0933.76016Borisov, A. V.; Lebedev, V. G. 15 1998 The dynamics of an articulated \(n\)-trailer vehicle. Zbl 1342.37064Bravo-Doddoli, Alejandro; García-Naranjo, Luis C. 15 2015 On detachment conditions in the problem on the motion of a rigid body on a rough plane. Zbl 1229.70015Ivanov, A. P. 15 2008 A generalization of Chaplygin’s reducibility theorem. Zbl 1229.37087Fernandez, O. E.; Mestdag, T.; Bloch, A. M. 15 2009 Euler configurations and quasi-polynomial systems. Zbl 1229.70032Albouy, A.; Fu, Y. 15 2007 Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability in the light of Kolmogorov and Nekhoroshev theories. Zbl 1390.70020Giorgilli, Antonio; Locatelli, Ugo; Sansottera, Marco 15 2017 The Euler-Jacobi-Lie integrability theorem. Zbl 1283.34035Kozlov, Valery V. 15 2013 Bifurcation diagrams of the Kowalevski top in two constant fields. Zbl 1133.70306Kharlamov, M. P. 15 2005 The ringing of Euler’s disk. Zbl 1013.70005Kessler, P.; O’Reilly, O. M. 15 2002 Dynamics and control of an omniwheel vehicle. Zbl 1367.70033Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 15 2015 Lie algebras in vortex dynamics and celestial mechanics. IV. Zbl 1076.76513Bolsinov, A. V.; Borisov, A. V.; Mamaev, I. S. 15 1999 Aspects of the planetary Birkhoff normal form. Zbl 1320.70007Pinzari, Gabriella 15 2013 The self-propulsion of a body with moving internal masses in a viscous fluid. Zbl 1329.70052Vetchanin, Evgeny V.; Mamaev, Ivan S.; Tenenev, Valentin A. 14 2013 Superintegrable systems on a sphere. Zbl 1077.37520Borisov, A. V.; Mamaev, I. S. 14 2005 The inertial motion of a roller racer. Zbl 1381.37076Bizyaev, Ivan A. 14 2017 Plate falling in a fluid: regular and chaotic dynamics of finite-dimensional models. Zbl 1327.34089Kuznetsov, Sergey P. 14 2015 On the problem of motion of vortex sources on a plane. Zbl 1164.37353Borisov, A. V.; Mamaev, I. S. 14 2006 Paul Painlevé and his contribution to science. Zbl 1333.01025Borisov, Alexey V.; Kudryashov, Nikolay A. 14 2014 Comments on the paper by A. V. Borisov, A. A. Kilin, I. S. Mamaev “How to control the Chaplygin ball using rotors. II”. Zbl 1353.70059Ivanova, Tatiana B.; Pivovarova, Elena N. 14 2014 Integrable Lotka-Volterra systems. Zbl 1229.37097Bogoyavlenskij, O. I. 14 2008 On cascades of elliptic periodic points in two-dimensional symplectic maps with homoclinic tangencies. Zbl 1229.37054Gonchenko, M. S.; Gonchenko, S. V. 14 2009 Polynomial entropies and integrable Hamiltonian systems. Zbl 1286.70022Marco, Jean-Pierre 14 2013 The dynamics of vortex rings: leapfrogging, choreographies and the stability problem. Zbl 1273.76067Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 13 2013 Bifurcation analysis and the Conley index in mechanics. Zbl 1252.76055Bolsinov, Alexey V.; Borisov, Alexey V.; Mamaev, Ivan S. 13 2012 A note on theorem of Massera. Zbl 1164.37314Zubelevich, O. 13 2006 A top on a vibrating base: new integrable problem of nonholonomic mechanics. Zbl 07507452Borisov, Alexey V.; Ivanov, Alexander P. 1 2022 Isochronicity in 1 DOF. Zbl 1484.34099Treschev, Dmitry V. 1 2022 Billiard ordered games and books. Zbl 1498.37092Dragović, Vladimir; Gasiorek, Sean; Radnović, Milena 1 2022 Geodesics in jet space. Zbl 07507462Bravo-Doddoli, Alejandro; Montgomery, Richard 1 2022 Darboux inversions of the Kepler problem. Zbl 07554441Albouy, Alain; Zhao, Lei 1 2022 On some aspects of the dynamics of a ball in a rotating surface of revolution and of the kasamawashi art. Zbl 07590473Fassò, Francesco; Sansonetto, Nicola 1 2022 Soliton solutions of high-order nonlinear Schrödinger equations with different laws of nonlinearities. Zbl 1473.35506Hosseini, Kamyar; Matinfar, Mashaallah; Mirzazadeh, Mohammad 7 2021 From Poincaré maps to Lagrangian descriptors: the case of the valley ridge inflection point potential. Zbl 1490.37101Crossley, Rebecca; Agaoglou, Makrina; Katsanikas, Matthaios; Wiggins, Stephen 4 2021 The time evolution of the trajectories after the selectivity in a symmetric potential energy surface with a post-transition-state bifurcation. Zbl 1490.37068Haigh, Douglas; Katsanikas, Matthaios; Agaoglou, Makrina; Wiggins, Stephen 3 2021 Compactness and index of ordinary central configurations for the curved \(n\)-body problem. Zbl 1491.70013Zhu, Shuqiang 2 2021 Ring configurations of point vortices in polar atmospheres. Zbl 1490.76056Dritschel, David G. 2 2021 Three-dimensional quasi-geostrophic staggered vortex arrays. Zbl 1479.76042Reinaud, Jean N. 2 2021 Uncertainty quantification of stochastic epidemic SIR models using B-spline polynomial chaos. Zbl 1471.92320Kaur, Navjot; Goyal, Kavita 2 2021 Classification of perturbations of Diophantine \(\mathbb{Z}^m\) actions on tori of arbitrary dimension. Zbl 1490.37085Petković, Boris 2 2021 Existence of a smooth Hamiltonian circle action near parabolic orbits and cuspidal tori. Zbl 1490.37080Kudryavtseva, Elena A.; Martynchuk, Nikolay N. 2 2021 A restricted four-body problem for the figure-eight choreography. Zbl 1475.34033Lara, Ricardo; Bengochea, Abimael 1 2021 Lax pairs and rational solutions of similarity reductions for Kupershmidt and Sawada-Kotera hierarchies. Zbl 1475.34055Kudryashov, Nikolay A. 1 2021 Recruitment effects on the evolution of epidemics in a simple SIR model. Zbl 1478.92213Nakamura, Gilberto; Grammaticos, Basil; Badoual, Mathilde 1 2021 Conservation laws for solitons in magneto-optic waveguides with anti-cubic and generalized anti-cubic nonlinearities. Zbl 1475.78007Biswas, Anjan; Kara, Abdul H.; Ekici, Mehmet; Zayed, Elsayed M. E.; Alzahrani, Abdullah K.; Belic, Milivoj R. 1 2021 Evolution of the singularities of the Schwarz function corresponding to the motion of a vortex patch in the two-dimensional Euler equations. Zbl 1479.76020Riccardi, Giorgio; Dritschel, David G. 1 2021 Parametric stability of a charged pendulum with an oscillating suspension point. Zbl 1493.70066Cruz Araujo, Gerson; Cabral, Hildeberto E. 1 2021 Integrals of motion in time-periodic Hamiltonian systems: the case of the Mathieu equation. Zbl 1487.70078Tzemos, Athanasios C.; Contopoulos, George 1 2021 The interaction of two unsteady point vortex sources in a deformation field in 2D incompressible flows. Zbl 1478.76073Vic, Armand; Carton, Xavier; Gula, Jonathan 1 2021 A particular integrable case in the nonautonomous problem of a Chaplygin sphere rolling on a vibrating plane. Zbl 1490.37079Kilin, Alexander A.; Pivovarova, Elena N. 1 2021 A new \((3+1)\)-dimensional Hirota bilinear equation: its Bäcklund transformation and rational-type solutions. Zbl 1450.37065Hosseini, Kamyar; Samavat, Majid; Mirzazadeh, Mohammad; Ma, Wen-Xiu; Hammouch, Zakia 12 2020 Highly dispersive optical solitons of an equation with arbitrary refractive index. Zbl 1471.35251Kudryashov, Nikolay A. 9 2020 Conservation laws for highly dispersive optical solitons in birefringent fibers. Zbl 1433.78019Biswas, Anjan; Kara, Abdul H.; Zhou, Qin; Alzahrani, Abdullah Kamis; Belic, Milivoj R. 5 2020 Dynamics of rubber Chaplygin sphere under periodic control. Zbl 1437.37082Mamaev, Ivan S.; Vetchanin, Evgeny V. 5 2020 Dynamics of the tippe top on a vibrating base. Zbl 1475.70007Borisov, Alexey V.; Ivanov, Alexander P. 5 2020 Stability and stabilization of steady rotations of a spherical robot on a vibrating base. Zbl 1475.70005Kilin, Alexander A.; Pivovarova, Elena N. 5 2020 Periodic controls in step 2 strictly convex sub-Finsler problems. Zbl 1473.49026Sachkov, Yuri L. 4 2020 On the nonlinear stability of the triangular points in the circular spatial restricted three-body problem. Zbl 1441.70004Cárcamo-Díaz, Daniela; Palacián, Jesús F.; Vidal, Claudio; Yanguas, Patricia 4 2020 Kovalevskaya exponents, weak Painlevé property and integrability for quasi-homogeneous differential systems. Zbl 1470.34004Huang, Kaiyin; Shi, Shaoyun; Li, Wenlei 4 2020 Confinement strategies in a simple SIR model. Zbl 1471.92337Nakamura, Gilberto; Grammaticos, Basil; Badoual, Mathilde 4 2020 Persistence of hyperbolic-type degenerate lower-dimensional invariant tori with prescribed frequencies in Hamiltonian systems. Zbl 1481.37067Xu, Junxiang; You, Jiangong 4 2020 Lax pairs and special polynomials associated with self-similar reductions of Sawada – Kotera and Kupershmidt equations. Zbl 1441.34096Kudryashov, Nikolay A. 3 2020 Revisiting the human and nature dynamics model. Zbl 1440.37083Grammaticos, Basil; Willox, Ralph; Satsuma, Junkichi 3 2020 The role of depth and flatness of a potential energy surface in chemical reaction dynamics. Zbl 1465.37070Lyu, Wenyang; Naik, Shibabrat; Wiggins, Stephen 2 2020 Chaos in Bohmian quantum mechanics: a short review. Zbl 1458.81024Contopoulos, George; Tzemos, Athanasios C. 1 2020 Dynamics and bifurcations on the normally hyperbolic invariant manifold of a periodically driven system with rank-1 saddle. Zbl 1458.37045Kuchelmeister, Manuel; Reiff, Johannes; Main, Jörg; Hernandez, Rigoberto 1 2020 Rational solutions of equations associated with the second Painlevé equation. Zbl 1451.34004Kudryashov, Nikolay A. 1 2020 Experimental results versus computer simulations of noisy Poincaré maps in an intermittency scenario. Zbl 1450.37072del Rio, Ezequiel; Elaskar, Sergio 1 2020 Two nonholonomic chaotic systems. I: On the Suslov problem. Zbl 1448.37075Borisov, Alexey V.; Mikishanina, Evgeniya A. 1 2020 Parametric stability of a pendulum with variable length in an elliptic orbit. Zbl 1465.70049de Menezes Neto, José Laudelino; Cabral, Hildeberto E. 1 2020 On the stability of potential systems under the action of non-conservative positional forces. Zbl 1464.70013Bulatovic, Ranislav M. 1 2020 Optical dromions and domain walls with the Kundu-Mukherjee-Naskar equation by the Laplace-Adomian decomposition scheme. Zbl 1448.65291González-Gaxiola, Oswaldo; Biswas, Anjan; Asma, Mir; Alzahrani, Abdullah Kamis 1 2020 The method of averaging for the Kapitza-Whitney pendulum. Zbl 1466.70020Polekhin, Ivan Yu. 1 2020 Nondegenerate Hamiltonian Hopf bifurcations in \(\omega:3:6\) resonance \((\omega=1\) or \(2)\). Zbl 1475.70019Mazrooei-Sebdani, Reza; Hakimi, Elham 1 2020 The tippedisk: a tippetop without rotational symmetry. Zbl 1475.70006Sailer, Simon; Eugster, Simon R.; Leine, Remco I. 1 2020 Quantifying the transition from spiral waves to spiral wave chimeras in a lattice of self-sustained oscillators. Zbl 1480.34053Shepelev, Igor A.; Bukh, Andrei V.; Muni, Sishu S.; Anishchenko, Vadim S. 1 2020 Dynamics of a spherical robot with variable moments of inertia and a displaced center of mass. Zbl 1483.70003Artemova, Elizaveta M.; Karavaev, Yury L.; Mamaev, Ivan S.; Vetchanin, Evgeny V. 1 2020 Caustics of Poncelet polygons and classical extremal polynomials. Zbl 1432.37055Dragović, Vladimir; Radnović, Milena 9 2019 Sub-Finsler geodesics on the Cartan group. Zbl 1412.49084Ardentov, Andrei A.; Le Donne, Enrico; Sachkov, Yuri L. 8 2019 Hamiltonization and separation of variables for a Chaplygin ball on a rotating plane. Zbl 1433.37065Tsiganov, Andrey V. 6 2019 Painlevé analysis and a solution to the traveling wave reduction of the Radhakrishnan-Kundu-Lakshmanan equation. Zbl 1434.78022Kudryashov, Nikolay A.; Safonova, Dariya V.; Biswas, Anjan 6 2019 Rational and special solutions for some Painlevé hierarchies. Zbl 1415.34132Kudryashov, Nikolay A. 5 2019 The dynamics of a Chaplygin sleigh with an elastic internal rotor. Zbl 1412.37066Fedonyuk, Vitaliy; Tallapragada, Phanindra 5 2019 Roaming at constant kinetic energy: Chesnavich’s model and the Hamiltonian isokinetic thermostat. Zbl 1436.37075Krajňák, Vladimír; Ezra, Gregory S.; Wiggins, Stephen 5 2019 Different models of rolling for a robot ball on a plane as a generalization of the Chaplygin ball problem. Zbl 1437.37078Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 5 2019 The Kepler problem: polynomial algebra of nonpolynomial first integrals. Zbl 1459.70041Tsiganov, Andrey V. 4 2019 Periodic billiards within conics in the Minkowski plane and Akhiezer polynomials. Zbl 1436.37036Adabrah, Anani Komla; Dragović, Vladimir; Radnović, Milena 4 2019 Evolution of Lagrangian manifolds and asymptotic solutions to the linearized equations of gas dynamics. Zbl 1412.35060Allilueva, Anna I.; Shafarevich, Andrei I. 3 2019 Euler elasticas for optimal control of the motion of mobile wheeled robots: the problem of experimental realization. Zbl 1431.49056Ardentov, Andrey A.; Karavaev, Yury L.; Yefremov, Kirill S. 3 2019 Qualitative analysis of the nonholonomic rolling of a rubber wheel with sharp edges. Zbl 1423.70013Kilin, Alexander A.; Pivovarova, Elena N. 3 2019 Impact of noise on the amplitude chimera lifetime in an ensemble of nonlocally coupled chaotic maps. Zbl 1479.39021Rybalova, Elena V.; Klyushina, Daria Y.; Anishchenko, Vadim S.; Strelkova, Galina I. 3 2019 V. I. Arnold’s “Pointwise” KAM theorem. Zbl 1435.37085Chierchia, L.; Koudjinan, C. E. 3 2019 Vortex pairs on the triaxial ellipsoid: axis equilibria stability. Zbl 1457.76078Koiller, Jair; Castilho, César; Rodrigues, Adriano Regis 2 2019 Integrability and chaos in vortex lattice dynamics. Zbl 1458.76021Kilin, Alexander A.; Artemova, Elizaveta M. 2 2019 On the motions of one near-autonomous Hamiltonian system at a 1:1:1 resonance. Zbl 1428.70037Kholostova, Olga V. 2 2019 On the normal force and static friction acting on a rolling ball actuated by internal point masses. Zbl 1433.37064Putkaradze, Vakhtang; Rogers, Stuart M. 2 2019 Stability of periodic solutions of the \(N\)-vortex problem in general domains. Zbl 1436.37065Gebhard, Björn; Ortega, Rafael 2 2019 Jumps of energy near a homoclinic set of a slowly time dependent Hamiltonian system. Zbl 1435.37084Bolotin, Sergey V. 2 2019 On the Chaplygin sphere in a magnetic field. Zbl 1435.37093Borisov, Alexey V.; Tsiganov, Andrey V. 2 2019 A note about integrable systems on low-dimensional Lie groups and Lie algebras. Zbl 1435.37082Bolsinov, Alexey; Bao, Jinrong 1 2019 Combinatorial Ricci flow for degenerate circle packing metrics. Zbl 1431.52031Pepa, Ruslan Yu.; Popelensky, Theodore Yu. 1 2019 On the constructive algorithm for stability analysis of an equilibrium point of a periodic Hamiltonian system with two degrees of freedom in the case of combinational resonance. Zbl 1430.37060Bardin, Boris S.; Chekina, Evgeniya A. 1 2019 On the volume elements of a manifold with transverse zeroes. Zbl 1435.53059Cardona, Robert; Miranda, Eva 1 2019 Singular reduction of the 2-body problem on the 3-sphere and the 4-dimensional spinning top. Zbl 1458.70005Arathoon, Philip 1 2019 Classical and quantum dynamics of a particle in a narrow angle. Zbl 1434.35135Dobrokhotov, Sergei Yu.; Minenkov, Dmitrii S.; Neishtadt, Anatoly I.; Shlosman, Semen B. 1 2019 Twisted states in a system of nonlinearly coupled phase oscillators. Zbl 1442.45003Bolotov, Dmitry; Bolotov, Maxim; Smirnov, Lev; Osipov, Grigory; Pikovsky, Arkady 1 2019 Topaj-Pikovsky involution in the Hamiltonian lattice of locally coupled oscillators. Zbl 1435.37099Kruglov, Vyacheslav P.; Kuznetsov, Sergey P. 1 2019 Integrability of the \(n\)-dimensional axially symmetric Chaplygin sphere. Zbl 1437.37081García-Naranjo, Luis C. 1 2019 Nonholonomic Noetherian symmetries and integrals of the Routh sphere and the Chaplygin ball. Zbl 1437.37079Bustamante, Miguel D.; Lynch, Peter 1 2019 Reduction of a Hamilton-Jacobi equation for nonholonomic systems. Zbl 1437.37080Esen, Oğul; Jiménez, Victor M.; de León, Manuel; Sardón, Cristina 1 2019 Synchronization of Chimera states in a network of many unidirectionally coupled layers of discrete maps. Zbl 1411.90070Strelkova, Galina I.; Vadivasova, Tatiana E.; Anishchenko, Vadim S. 16 2018 Exotic dynamics of nonholonomic roller racer with periodic control. Zbl 1412.37064Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 16 2018 Linear Hamiltonian systems: quadratic integrals, singular subspaces and stability. Zbl 1400.37061Kozlov, Valery V. 13 2018 Chaos and hyperchaos in coupled antiphase driven Toda oscillators. Zbl 1398.37031Stankevich, Nataliya V.; Dvorak, Anton; Astakhov, Vladimir; Jaros, Patrycja; Kapitaniak, Marcin; Perlikowski, Przemysław; Kapitaniak, Tomasz 12 2018 Dynamics-based motion planning for a pendulum-actuated spherical rolling robot. Zbl 1411.70021Bai, Yang; Svinin, Mikhail; Yamamoto, Motoji 10 2018 Asymptotic and exact solutions of the Fitzhugh-Nagumo model. Zbl 1401.34004Kudryashov, Nikolay A. 9 2018 Exact solutions and integrability of the Duffing-van der Pol equation. Zbl 1425.34105Kudryashov, Nikolay A. 8 2018 Comparing dynamics initiated by an attached oscillating particle for the nonholonomic model of a Chaplygin sleigh and for a model with strong transverse and weak longitudinal viscous friction applied at a fixed point on the body. Zbl 1412.37065Borisov, Alexey V.; Kuznetsov, Sergey P. 8 2018 Self-propulsion of a smooth body in a viscous fluid under periodic oscillations of a rotor and circulation. Zbl 1412.37076Borisov, Alexey V.; Mamaev, Ivan S.; Vetchanin, Evgeny V. 8 2018 Regular and chaotic dynamics of a Chaplygin sleigh due to periodic switch of the nonholonomic constraint. Zbl 1400.37076Kuznetsov, Sergey P. 7 2018 Dynamics of a smooth profile in a medium with friction in the presence of parametric excitation. Zbl 1411.70027Borisov, Alexey V.; Mamaev, Ivan S.; Vetchanin, Eugeny V. 7 2018 Persistence properties of normally hyperbolic Tori. Zbl 1400.37067Broer, Henk; Hanßmann, Heinz; Wagener, Florian 6 2018 Finite-time collapse of three point vortices in the plane. Zbl 1411.70011Krishnamurthy, Vikas S.; Stremler, Mark A. 6 2018 A nonholonomic model of the Paul trap. Zbl 1400.37075Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 5 2018 The application of Lagrangian descriptors to 3D vector fields. Zbl 1412.37057García-Garrido, Víctor J.; Curbelo, Jezabel; Mancho, Ana M.; Wiggins, Stephen; Mechoso, Carlos R. 5 2018 Detection of phase space structures of the cat map with Lagrangian descriptors. Zbl 1412.37062García-Garrido, Víctor J.; Balibrea-Iniesta, Francisco; Wiggins, Stephen; Mancho, Ana M.; Lopesino, Carlos 5 2018 ...and 741 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,000 Authors 109 Borisov, Alekseĭ Vladimirovich 99 Mamaev, Ivan Sergeevich 63 Kudryashov, Nikolaĭ Alekseevich 60 Tsyganov, Andreĭ Vladimirovich 50 Kilin, Aleksandr Aleksandrovich 34 Bizyaev, Ivan Alekseevich 34 Wiggins, Stephen 33 Xu, Junxiang 29 Gonchenko, Sergey V. 28 Kozlov, Valeriĭ Vasil’evich 26 Vidal, Claudio 25 Llibre, Jaume 25 Przybylska, Maria 24 Dragović, Vladimir 22 Kuznetsov, Sergey P. 22 Matveev, Vladimir S. 22 Simó, Carles 22 Zhang, Dongfeng 21 Turaev, Dmitry V. 20 Kazakov, Alexey O. 19 Broer, Henk W. 19 García-Naranjo, Luis C. 19 Maciejewski, Andrzej J. 19 Vetchanin, Evgeniĭ Vladimirovich 17 Bolsinov, Alexey V. 17 Bounemoura, Abed Bounemoura 17 Sinelshchikov, Dmitry I. 16 Bardin, Boris Sabirovich 16 Dullin, Holger R. 16 Ryabov, Pavel Evgen’evich 15 Gonchenko, Marina S. 15 Grammaticos, Basil 15 Kurakin, Leonid Gennadievich 15 Meiss, James D. 14 Delshams, Amadeu 14 Guzzo, Massimiliano 14 Mireles-James, Jason D. 13 Biswas, Anjan 13 Palacián, Jesús F. 13 Pivovarova, Elena Nikolaevna 13 Yanguas, Patricia 12 Hanßmann, Heinz 12 Ivanov, Aleksandr Pavlovich 12 Kizner, Ziv 12 Ramani, Alfred 12 Sokolov, Sergeĭ Viktorovich 12 Strelkova, Galina Ivanova 12 Valiquette, Francis 11 de la Llave, Rafael 11 Fassò, Francesco 11 Karavaev, Yurĭ Leonidovich 11 Katsanikas, Matthaios 11 Petrera, Matteo 11 Pinzari, Gabriella 11 Sataev, Igor’ Rustamovich 11 Suris, Yuri Borisovich 11 Vedyushkina, Viktoriya Viktorovna 10 Anishchenko, Vadim Semenovich 10 Corbera, Montserrat 10 García-Garrido, Víctor J. 10 Gonchenko, Aleksandr Sergeevich 10 Jovanović, Božidar Žarko 10 Koiller, Jair 10 Mikishanina, Evgeniya Arifzhanovna 10 Newton, Paul K. 10 Pérez-Chavela, Ernesto 10 Radnović, Milena 10 Sansottera, Marco 10 Vieiro, Arturo 9 Balseiro, Paula 9 Bolotin, Sergeĭ Vladimirovich 9 Burov, Aleksandr Anatol’evich 9 Carton, Xavier J. 9 Fedorov, Yuri N. 9 Fomenko, Anatoliĭ Timofeevich 9 Gutkin, Eugene 9 Kanso, Eva Adnan 9 Locatelli, Ugo 9 Miranda, Eva 9 Reinaud, Jean N. 9 Rozikov, Utkir A. 9 Sachkov, Yuriĭ Leonidovich 9 Sansonetto, Nicola 9 Sevryuk, Mikhail Borisovich 9 Valls Anglés, Cláudia 9 Vanhaecke, Pol 9 Wang, Xiaocai 9 Zhu, Shuqiang 8 Belić, Milivoj R. 8 Berti, Massimiliano 8 Bloch, Anthony Michael 8 Celletti, Alessandra 8 Damianou, Pantelis Andrea 8 Falqui, Gregorio 8 Ferrer, Sebastián 8 Gajić, Borislav 8 Kaloshin, Vadim Yu. 8 Kharlamov, Mikhail Pavlovich 8 Koshel, Konstantin V. 8 Montaldi, James A. ...and 2,900 more Authors all top 5 Cited in 385 Journals 454 Regular and Chaotic Dynamics 105 Physica D 83 Chaos 76 Journal of Mathematical Physics 71 Journal of Differential Equations 69 Celestial Mechanics and Dynamical Astronomy 65 Journal of Geometry and Physics 64 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 61 Russian Journal of Nonlinear Dynamics 57 Communications in Nonlinear Science and Numerical Simulation 53 Journal of Nonlinear Science 41 Communications in Mathematical Physics 41 Nonlinearity 40 Chaos, Solitons and Fractals 40 Discrete and Continuous Dynamical Systems 37 Theoretical and Mathematical Physics 36 Journal of Mathematical Analysis and Applications 33 Applied Mathematics and Computation 32 Physics Letters. 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