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Experimental Mathematics Volume 8, 1999 - Issue 1
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Original Articles

Singular Separatrix Splitting and the Melnikov Method: An Experimental Study

Amadeu Delshams Departament de Maternática Aplicada I, Universitat Politécnica de Catalunya, Diagonal 647, 08028, Barcelona, Spain E-mail: [email protected]
&
Rafael Ramírez-Ros Departament de Matemática Aplicada I, Universitat Politécnica de Catalunya, Diagonal 647, 08028, Barcelona, Spain E-mail: [email protected]
Pages 29-48 | Published online: 03 Apr 2012

Citations (12)

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Read on this site (1)

P. Martín, R. Ramírez-Ros & A. Tamarit-Sariol. (2016) Exponentially Small Asymptotic Formulas for the Length Spectrum in Some Billiard Tables. Experimental Mathematics 25:4, pages 416-440.
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Articles from other publishers (11)

E Fontich, C Simó & A Vieiro. (2019) Splitting of the separatrices after a Hamiltonian–Hopf bifurcation under periodic forcing. Nonlinearity 32:4, pages 1440-1493.
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I. Baldomá, O. Castejón & T. M. Seara. (2018) Breakdown of a 2D Heteroclinic Connection in the Hopf-Zero Singularity (I). Journal of Nonlinear Science 28:5, pages 1551-1627.
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Yu.A. Kubyshin, O. Larreal, R. Ram?rez-Ros & T.M. Seara. (2017) Stability of the phase motion in race-track microtrons. Physica D: Nonlinear Phenomena 349, pages 12-26.
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Àlex Haro, Marta Canadell, Jordi-Lluis Figueras, Alejandro Luque & Josep Maria MondeloÀlex Haro. 2016. The Parameterization Method for Invariant Manifolds. The Parameterization Method for Invariant Manifolds 1 28 .
Inmaculada Baldom?Ernest Fontich, Marcel Guardia & Tere M. Seara. (2012) Exponentially small splitting of separatrices beyond Melnikov analysis: Rigorous results. Journal of Differential Equations 253:12, pages 3304-3439.
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I. Baldom?P. Mart?n. (2012) The Inner Equation for Generalized Standard Maps. SIAM Journal on Applied Dynamical Systems 11:3, pages 1062-1097.
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Yong-Guo Shi & Li Chen. (2011) Reversible maps and their symmetry lines. Communications in Nonlinear Science and Numerical Simulation 16:1, pages 363-371.
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Rafael Ram?rez-Ros. (2005) Exponentially small separatrix splittings and almost invisible homoclinic bifurcations in some billiard tables. Physica D: Nonlinear Phenomena 210:3-4, pages 149-179.
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Vassili Gelfreich. (2002) Near strongly resonant periodic orbits in a Hamiltonian system. Proceedings of the National Academy of Sciences 99:22, pages 13975-13979.
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Amadeu Delshams, Yuri Fedorov & Rafael Ramírez-Ros. (2001) Homoclinic billiard orbits inside symmetrically perturbed ellipsoids. Nonlinearity 14:5, pages 1141-1195.
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H?ctor E. Lomel??James D. Meiss. (2000) Heteroclinic orbits and Flux in a perturbed integrable Suris map. Physics Letters A 269:5-6, pages 309-318.
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