An alternative method to estimate the splitting of separatrices for the discretized pendulum equation

DOI10.3233/ASY-151326zbMath1337.65070MaRDI QIDQ5744775

Hocine Sellama

Publication date: 19 February 2016

Published in: Asymptotic Analysis (Search for Journal in Brave)

zbMATH Keywords

manifoldsformal solutionlinear operatorquasi-solutiondifference equationGevrey asymptotic

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability of solutions to ordinary differential equations (34D20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Additive difference equations (39A10) Discrete version of topics in analysis (39A12) Numerical investigation of stability of solutions to ordinary differential equations (65L07) Finite difference and finite volume methods for ordinary differential equations (65L12) Stability theory for difference equations (39A30) Kinematics of a particle (70B05)

Cites Work

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• A proof of the exponentially small transversality of the separatrices for the standard map
• Splitting of separatrices for standard and semistandard mappings
• Résurgence paramétrique et exponentielle petitesse de l'écart des séparatrices du pendule rapidement forcé. (Parametric resurgence and exponential smallness of the splitting of the separatrices of the rapidly forced pendulum.)
• On the distance between separatrices for the discretized logistic differential equation
• On the complex separatrices of some standard-like maps
• Gevrey solutions of singularly perturbed differential equations