Fontich, E.; Simó, C.; Vieiro, A. Splitting of the separatrices after a Hamiltonian-Hopf bifurcation under periodic forcing. (English) Zbl 1409.37059 Nonlinearity 32, No. 4, 1440-1493 (2019). Reviewer: Stathis Antoniou (Athína) MSC: 37J20 37J40 37J45 37C29 PDFBibTeX XMLCite \textit{E. Fontich} et al., Nonlinearity 32, No. 4, 1440--1493 (2019; Zbl 1409.37059) Full Text: DOI arXiv
Simó, Carles Some questions looking for answers in dynamical systems. (English) Zbl 07694266 Discrete Contin. Dyn. Syst. 38, No. 12, 6215-6239 (2018). MSC: 00A27 37C29 37C45 37C55 37C70 37D45 37J30 37J40 37N05 70F10 70F16 37M05 37M25 PDFBibTeX XMLCite \textit{C. Simó}, Discrete Contin. Dyn. Syst. 38, No. 12, 6215--6239 (2018; Zbl 07694266) Full Text: DOI
Fontich, Ernest; Simó, Carles; Vieiro, Arturo On the “hidden” harmonics associated to best approximants due to quasi-periodicity in splitting phenomena. (English) Zbl 1410.37023 Regul. Chaotic Dyn. 23, No. 6, 638-653 (2018). MSC: 37C55 37J40 37J45 PDFBibTeX XMLCite \textit{E. Fontich} et al., Regul. Chaotic Dyn. 23, No. 6, 638--653 (2018; Zbl 1410.37023) Full Text: DOI
Meiss, James D.; Miguel, Narcís; Simó, Carles; Vieiro, Arturo Accelerator modes and anomalous diffusion in 3D volume-preserving maps. (English) Zbl 1409.37060 Nonlinearity 31, No. 12, 5615-5642 (2018). MSC: 37J20 37C05 37G10 37J40 PDFBibTeX XMLCite \textit{J. D. Meiss} et al., Nonlinearity 31, No. 12, 5615--5642 (2018; Zbl 1409.37060) Full Text: DOI arXiv
Kapela, Tomasz; Simó, Carles Rigorous KAM results around arbitrary periodic orbits for Hamiltonian systems. (English) Zbl 1412.70024 Nonlinearity 30, No. 3, 965-986 (2017). MSC: 70H08 70F10 37J40 37J25 PDFBibTeX XMLCite \textit{T. Kapela} and \textit{C. Simó}, Nonlinearity 30, No. 3, 965--986 (2017; Zbl 1412.70024) Full Text: DOI arXiv
Simó, Carles Dynamical properties of Hamiltonian systems with applications to celestial mechanics. (English) Zbl 1373.70010 Corbera, Montserrat (ed.) et al., Central configurations, periodic orbits, and Hamiltonian systems. Lecture notes given at the research program on central configurations, periodic orbits and beyond in celestial mechanics, Barcelona, Spain, January 27–31, 2014. Basel: Birkhäuser/Springer (ISBN 978-3-0348-0932-0/pbk; 978-3-0348-0933-7/ebook). Advanced Courses in Mathematics – CRM Barcelona, 169-232 (2016). Reviewer: Martha Alvarez-Ramirez (México City) MSC: 70F10 70F15 37N05 37J40 70H08 PDFBibTeX XMLCite \textit{C. Simó}, in: Central configurations, periodic orbits, and Hamiltonian systems. Lecture notes given at the research program on central configurations, periodic orbits and beyond in celestial mechanics, Barcelona, Spain, January 27--31, 2014. Basel: Birkhäuser/Springer. 169--232 (2016; Zbl 1373.70010) Full Text: DOI
Corbera, Montserrat (ed.); Cors, Josep Maria (ed.); Ponce, Enrique (ed.) [Llibre, Jaume; Moeckel, Richard; Simó, Carles] Central configurations, periodic orbits, and Hamiltonian systems. Lecture notes given at the research program on central configurations, periodic orbits and beyond in celestial mechanics, Barcelona, Spain, January 27–31, 2014. (English) Zbl 1336.37002 Advanced Courses in Mathematics – CRM Barcelona. Basel: Birkhäuser/Springer (ISBN 978-3-0348-0932-0/pbk; 978-3-0348-0933-7/ebook). viii, 232 p. (2016). MSC: 37-06 37J10 37J15 37J40 37J45 37N05 34C25 70F10 70F15 00B25 PDFBibTeX XMLCite \textit{M. Corbera} (ed.) et al., Central configurations, periodic orbits, and Hamiltonian systems. Lecture notes given at the research program on central configurations, periodic orbits and beyond in celestial mechanics, Barcelona, Spain, January 27--31, 2014. Basel: Birkhäuser/Springer (2016; Zbl 1336.37002) Full Text: DOI
Simó, Carles Measuring the total amount of chaos in some Hamiltonian systems. (English) Zbl 1299.70032 Discrete Contin. Dyn. Syst. 34, No. 12, 5135-5164 (2014). MSC: 70H07 70K70 37N05 34D08 37J40 37J45 37M25 PDFBibTeX XMLCite \textit{C. Simó}, Discrete Contin. Dyn. Syst. 34, No. 12, 5135--5164 (2014; Zbl 1299.70032) Full Text: DOI
Dumortier, Freddy; Ibáñez, Santiago; Kokubu, Hiroshi; Simó, Carles About the unfolding of a Hopf-zero singularity. (English) Zbl 1283.34039 Discrete Contin. Dyn. Syst. 33, No. 10, 4435-4471 (2013). MSC: 34C23 34C37 34C28 34C20 34A34 PDFBibTeX XMLCite \textit{F. Dumortier} et al., Discrete Contin. Dyn. Syst. 33, No. 10, 4435--4471 (2013; Zbl 1283.34039) Full Text: DOI
Gelfreich, V.; Simó, C.; Vieiro, A. Dynamics of 4D symplectic maps near a double resonance. (English) Zbl 1353.37113 Physica D 243, No. 1, 92-110 (2013). MSC: 37J10 37J45 70K30 PDFBibTeX XMLCite \textit{V. Gelfreich} et al., Physica D 243, No. 1, 92--110 (2013; Zbl 1353.37113) Full Text: DOI
Hanßmann, Heinz; Simó, Carles Dynamical stability of quasi-periodic response solutions in planar conservative systems. (English) Zbl 1287.37035 Indag. Math., New Ser. 23, No. 3, 151-166 (2012). MSC: 37J25 37J40 37J45 37C60 PDFBibTeX XMLCite \textit{H. Hanßmann} and \textit{C. Simó}, Indag. Math., New Ser. 23, No. 3, 151--166 (2012; Zbl 1287.37035) Full Text: DOI
Martínez, Regina; Simó, Carles Non-integrability of the degenerate cases of the swinging Atwood’s machine using higher order variational equations. (English) Zbl 1211.37069 Discrete Contin. Dyn. Syst. 29, No. 1, 1-24 (2011). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 37J30 70H07 34M35 PDFBibTeX XMLCite \textit{R. Martínez} and \textit{C. Simó}, Discrete Contin. Dyn. Syst. 29, No. 1, 1--24 (2011; Zbl 1211.37069) Full Text: DOI
Simó, C.; Vieiro, A. Planar radial weakly dissipative diffeomorphisms. (English) Zbl 1311.37059 Chaos 20, No. 4, 043138, 18 p. (2010). MSC: 37L50 37L10 PDFBibTeX XMLCite \textit{C. Simó} and \textit{A. Vieiro}, Chaos 20, No. 4, 043138, 18 p. (2010; Zbl 1311.37059) Full Text: DOI
Martínez, R.; Simó, C. Non-integrability of Hamiltonian systems through high order variational equations: summary of results and examples. (English) Zbl 1229.37058 Regul. Chaotic Dyn. 14, No. 3, 323-348 (2009). MSC: 37J30 70H07 34M35 PDFBibTeX XMLCite \textit{R. Martínez} and \textit{C. Simó}, Regul. Chaotic Dyn. 14, No. 3, 323--348 (2009; Zbl 1229.37058) Full Text: DOI
Simó, Carles Some properties of the global behaviour of conservative low-dimensional systems. (English) Zbl 1188.37019 Cucker, Felipe (ed.) et al., Foundations of computational mathematics, Hong Kong, China, 2008. Selected papers based on the presentations at the international conference of the Society for the Foundations of Computational Mathematics (FoCM), June 16–26, 2008. Cambridge: Cambridge University Press (ISBN 978-0-521-73970-2/pbk). London Mathematical Society Lecture Note Series 363, 162-189 (2009). Reviewer: Alois Klíč (Praha) MSC: 37C10 37J05 37G05 37C75 34C23 70F07 PDFBibTeX XMLCite \textit{C. Simó}, Lond. Math. Soc. Lect. Note Ser. 363, 162--189 (2009; Zbl 1188.37019)
Simó, C.; Vieiro, A. Resonant zones, inner and outer splittings in generic and low order resonances of area preserving maps. (English) Zbl 1181.37077 Nonlinearity 22, No. 5, 1191-1245 (2009). Reviewer: Yuri E. Gliklikh (Voronezh) MSC: 37J10 37G05 37G10 37C29 37M99 37J40 PDFBibTeX XMLCite \textit{C. Simó} and \textit{A. Vieiro}, Nonlinearity 22, No. 5, 1191--1245 (2009; Zbl 1181.37077) Full Text: DOI
Simó, Carles; Treschev, Dmitri Stability islands in the vicinity of separatrices of near-integrable symplectic maps. (English) Zbl 1153.37406 Discrete Contin. Dyn. Syst., Ser. B 10, No. 2-3, 681-698 (2008). MSC: 37J40 70K44 70H08 PDFBibTeX XMLCite \textit{C. Simó} and \textit{D. Treschev}, Discrete Contin. Dyn. Syst., Ser. B 10, No. 2--3, 681--698 (2008; Zbl 1153.37406) Full Text: DOI
Morales-Ruiz, Juan J.; Ramis, Jean-Pierre; Simó, Carles Integrability of Hamiltonian systems and differential Galois groups of higher variational equations. (English) Zbl 1144.37023 Ann. Sci. Éc. Norm. Supér. (4) 40, No. 6, 845-884 (2007). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 37J30 37J35 12H05 37F10 34M35 PDFBibTeX XMLCite \textit{J. J. Morales-Ruiz} et al., Ann. Sci. Éc. Norm. Supér. (4) 40, No. 6, 845--884 (2007; Zbl 1144.37023) Full Text: DOI Numdam EuDML
Martínez, Regina; Samà, Anna; Simó, Carles Analysis of the stability of a family of singular-limit linear periodic systems in \(\mathbb {R}^4\). Applications. (English) Zbl 1111.34033 J. Differ. Equations 226, No. 2, 652-686 (2006). Reviewer: Alois Steindl (Wien) MSC: 34C15 34C37 34C23 34D05 37J20 37J25 37J40 PDFBibTeX XMLCite \textit{R. Martínez} et al., J. Differ. Equations 226, No. 2, 652--686 (2006; Zbl 1111.34033) Full Text: DOI
Martínez, Regina; Samà, Anna; Simó, Carles Stability diagram for 4D linear periodic systems with applications to homographic solutions. (English) Zbl 1108.34032 J. Differ. Equations 226, No. 2, 619-651 (2006). Reviewer: Alois Steindl (Wien) MSC: 34C20 34C25 34D05 37G05 37J25 37J40 PDFBibTeX XMLCite \textit{R. Martínez} et al., J. Differ. Equations 226, No. 2, 619--651 (2006; Zbl 1108.34032) Full Text: DOI
Puig, Joaquim; Simó, Carles Analytic families of reducible linear quasi-periodic differential equations. (English) Zbl 1105.34021 Ergodic Theory Dyn. Syst. 26, No. 2, 481-524 (2006). Reviewer: Natalia Medvedeva (Chelyabinsk) MSC: 34C20 34A30 34B30 34L40 47E05 34-02 34L05 PDFBibTeX XMLCite \textit{J. Puig} and \textit{C. Simó}, Ergodic Theory Dyn. Syst. 26, No. 2, 481--524 (2006; Zbl 1105.34021) Full Text: DOI
Broer, H. W.; Hoveijn, I.; van Noort, M.; Simó, C.; Vegter, G. The parametrically forced pendulum: A case study in \(1\frac12\) degree of freedom. (English) Zbl 1061.37039 J. Dyn. Differ. Equations 16, No. 4, 897-947 (2004). Reviewer: Irina V. Konopleva (Ul’yanovsk) MSC: 37J20 37J40 37M20 70H08 PDFBibTeX XMLCite \textit{H. W. Broer} et al., J. Dyn. Differ. Equations 16, No. 4, 897--947 (2004; Zbl 1061.37039) Full Text: DOI
Broer, Henk; Puig, Joaquim; Simó, Carles Resonance tongues and instability pockets in the quasi-periodic Hill-Schrödinger equation. (English) Zbl 1098.37014 Commun. Math. Phys. 241, No. 2-3, 467-503 (2003). MSC: 37B55 34B30 34C20 34C28 34C29 37E45 PDFBibTeX XMLCite \textit{H. Broer} et al., Commun. Math. Phys. 241, No. 2--3, 467--503 (2003; Zbl 1098.37014) Full Text: DOI
Simó, Carles; Valls, Clàudia A formal approximation of the splitting of separatrices in the classical Arnold’s example of diffusion with two equal parameters. (English) Zbl 1001.37051 Nonlinearity 14, No. 6, 1707-1760 (2001). Reviewer: Messoud Efendiev (Berlin) MSC: 37J40 37M99 70H08 PDFBibTeX XMLCite \textit{C. Simó} and \textit{C. Valls}, Nonlinearity 14, No. 6, 1707--1760 (2001; Zbl 1001.37051) Full Text: DOI
Gómez, G.; Jorba, À.; Simó, C.; Masdemont, J. Dynamics and mission design near libration points. Vol. 4: Advanced methods for triangular points. (English) Zbl 0969.70002 World Scientific Monograph Series in Mathematics. 5. Singapore: World Scientific. x, 262 p. £41.00 (2001). Reviewer: Nina A.Solovaya (Moskva) MSC: 70-02 70F15 70F07 70F05 70M20 PDFBibTeX XMLCite \textit{G. Gómez} et al., Dynamics and mission design near libration points. Vol. 4: Advanced methods for triangular points. Singapore: World Scientific (2001; Zbl 0969.70002) Full Text: DOI
Broer, H. W.; Simó, C. Reducible linear quasi-periodic systems with positive Lyapunov exponent and varying rotation number. (English) Zbl 0970.34039 J. Differ. Equations 168, No. 1, 60-66 (2000). Reviewer: Stefan Siegmund (Augsburg) MSC: 34C27 34D08 34C20 34A30 34C25 PDFBibTeX XMLCite \textit{H. W. Broer} and \textit{C. Simó}, J. Differ. Equations 168, No. 1, 60--66 (2000; Zbl 0970.34039) Full Text: DOI Link
Broer, Henk; Simó, Carles Resonance tongues in Hill’s equations: A geometric approach. (English) Zbl 1046.34072 J. Differ. Equations 166, No. 2, 290-327 (2000). MSC: 34C29 34A30 34C20 70J40 PDFBibTeX XMLCite \textit{H. Broer} and \textit{C. Simó}, J. Differ. Equations 166, No. 2, 290--327 (2000; Zbl 1046.34072) Full Text: DOI Link
Simó, C.; Stuchi, T. J. Central stable/unstable manifolds and the destruction of KAM tori in the planar Hill problem. (English) Zbl 0963.37052 Physica D 140, No. 1-2, 1-32 (2000). Reviewer: Messoud Efendiev (Berlin) MSC: 37J40 37D10 PDFBibTeX XMLCite \textit{C. Simó} and \textit{T. J. Stuchi}, Physica D 140, No. 1--2, 1--32 (2000; Zbl 0963.37052) Full Text: DOI
Simó, C. Invariant curves of analytic perturbed nontwist area preserving maps. (English) Zbl 0932.37048 Regul. Chaotic Dyn. 3, No. 3, 180-195 (1998). MSC: 37J40 37E40 37J35 PDFBibTeX XMLCite \textit{C. Simó}, Regul. Chaotic Dyn. 3, No. 3, 180--195 (1998; Zbl 0932.37048)
Broer, Henk; Simó, Carles; Tatjer, Joan Carles Towards global models near homoclinic tangencies of dissipative diffeomorphisms. (English) Zbl 0937.37013 Nonlinearity 11, No. 3, 667-770 (1998). Reviewer: Ale Jan Homburg (Utrecht) MSC: 37D45 37D30 PDFBibTeX XMLCite \textit{H. Broer} et al., Nonlinearity 11, No. 3, 667--770 (1998; Zbl 0937.37013) Full Text: DOI Link
Broer, Henk; Roussarrie, Robert; Simó, Carles Invariant circles in the Bogdanov-Takens bifurcation for diffeomorphisms. (English) Zbl 0876.58032 Ergodic Theory Dyn. Syst. 16, No. 6, 1147-1172 (1996). Reviewer: C.Chicone (Columbia) MSC: 37G99 37G05 37A99 PDFBibTeX XMLCite \textit{H. Broer} et al., Ergodic Theory Dyn. Syst. 16, No. 6, 1147--1172 (1996; Zbl 0876.58032) Full Text: DOI
Jorba, Àngel; Simó, Carles On quasi-periodic perturbations of elliptic equilibrium points. (English) Zbl 0863.34043 SIAM J. Math. Anal. 27, No. 6, 1704-1737 (1996). Reviewer: P.Smith (Keele) MSC: 34C27 34D10 34C99 37C55 37J40 37J99 PDFBibTeX XMLCite \textit{À. Jorba} and \textit{C. Simó}, SIAM J. Math. Anal. 27, No. 6, 1704--1737 (1996; Zbl 0863.34043) Full Text: DOI
Morales-Ruiz, Juan J.; Simó, Carles Non-integrability criteria for Hamiltonians in the case of Lamé normal variational equations. (English) Zbl 0866.58034 J. Differ. Equations 129, No. 1, 111-135 (1996); corrigendum ibid. 144, No. 2, 477-478 (1998). Reviewer: G.V.Khmelevskaja-Plotnikova (Namur) MSC: 37J30 37K05 34M15 PDFBibTeX XMLCite \textit{J. J. Morales-Ruiz} and \textit{C. Simó}, J. Differ. Equations 129, No. 1, 111--135 (1996; Zbl 0866.58034) Full Text: DOI
Broer, H. W.; Roussarie, R.; Simó, C. On the Bogdanov-Takens bifurcation for planar diffeomorphisms. (English) Zbl 0938.37512 Perelló, C. (ed.) et al., International conference on differential equations. Vol. 1, 2. Proceedings of the conference, EQUADIFF 91, Barcelona, Spain, August 26-31, 1991. Singapore: World Scientific. 81-92 (1993). MSC: 37G05 PDFBibTeX XMLCite \textit{H. W. Broer} et al., in: International conference on differential equations. Vol. 1, 2. Proceedings of the conference, EQUADIFF 91, Barcelona, Spain, August 26-31, 1991. Singapore: World Scientific. 81--92 (1993; Zbl 0938.37512)
Olvera, Arturo; Simó, Carles Elliptic non-Birkhoff periodic orbits in the twist maps. (English) Zbl 0870.58088 Int. J. Bifurcation Chaos Appl. Sci. Eng. 3, No. 1, 165-185 (1993). MSC: 37J40 37G99 PDFBibTeX XMLCite \textit{A. Olvera} and \textit{C. Simó}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 3, No. 1, 165--185 (1993; Zbl 0870.58088) Full Text: DOI
Jorba, Àngel; Simó, Carles On the reducibility of linear differential equations with quasiperiodic coefficients. (English) Zbl 0761.34026 J. Differ. Equations 98, No. 1, 111-124 (1992). Reviewer: S.Staněk (Olomouc) MSC: 34C20 34A30 34C27 PDFBibTeX XMLCite \textit{À. Jorba} and \textit{C. Simó}, J. Differ. Equations 98, No. 1, 111--124 (1992; Zbl 0761.34026) Full Text: DOI
Fontich, E.; Simó, C. The splitting of separatrices for analytic diffeomorphisms. (English) Zbl 0706.58061 Ergodic Theory Dyn. Syst. 10, No. 2, 295-318 (1990). Reviewer: L.Maxim-Răileanu MSC: 37C80 37C10 37D99 PDFBibTeX XMLCite \textit{E. Fontich} and \textit{C. Simó}, Ergodic Theory Dyn. Syst. 10, No. 2, 295--318 (1990; Zbl 0706.58061)
Olvera, Arturo; Simó, Carles The obstruction method and some numerical experiments related to the standard map. (English) Zbl 0628.58046 Periodic solutions of Hamiltonian systems and related topics, Proc. NATO Adv. Res. Workshop, Il Ciocco/Italy 1986, NATO ASI Ser., Ser. C 209, 235-244 (1987). MSC: 37G99 37C80 37J40 PDFBibTeX XML
Olvera, Arturo; Simó, Carles An obstruction method for the destruction of invariant curves. (English) Zbl 0612.58039 Physica D 26, 181-192 (1987). MSC: 37J40 PDFBibTeX XMLCite \textit{A. Olvera} and \textit{C. Simó}, Physica D 26, 181--192 (1987; Zbl 0612.58039) Full Text: DOI
Simo, C.; Fontich, E. On the smallness of the angle between split separatrices. (English) Zbl 0626.58009 Singularités, feuilletages et mécanique hamiltonienne, Rencontre Balaruc/France 1983, Sémin. sud-rhodanien Géom., 41-52 (1985). Reviewer: I.Ya.Dorfman MSC: 37J40 37G99 37J35 37K10 37J99 PDFBibTeX XML
Simo, Carles Stability of degenerate fixed points of analytic area preserving mappings. (English) Zbl 0516.58028 Astérisque 98-99, 184-194 (1983). MSC: 37C75 34D20 28D05 PDFBibTeX XMLCite \textit{C. Simo}, Astérisque 98--99, 184--194 (1983; Zbl 0516.58028)
Simó, Carles Connection of invariant manifolds in the \(n\)-body problem, \(n>3\). Rev. Univ. Santander No. 2, Part 2. (Spanish) Zbl 0938.37511 Proceedings of the 6th conference of Portuguese and Spanish mathematicians, Santander, Spain, June 5-8, 1979. Part II. Santander: Univ. Santander, 1257-1261 (1979). MSC: 37G05 37J25 70F10 PDFBibTeX XMLCite \textit{C. Simó}, in: Actas de las VI jornadas de matemáticas hispano-lusas. Part II. Santander: Univ. Santander. 1257--1261 (1979; Zbl 0938.37511)