Exponentially small upper bounds for the splitting of separatrices for high frequency periodic perturbations

DOI10.1016/0362-546X(93)90031-MzbMath0773.34042OpenAlexW2010235954MaRDI QIDQ4694498

Ernest Fontich

Publication date: 18 October 1993

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(93)90031-m

zbMATH Keywords

homoclinic solutionsplitting of separatricesmaximum separationexponentially smallintersections of the invariant manifolds

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items

Exponentially small splitting for the pendulum: A classical problem revisited ⋮ NUMERICAL COMPUTATION OF HOMOCLINIC ORBITS FOR FLOWS ⋮ Exponentially small splitting of separatrices beyond Melnikov analysis: Rigorous results ⋮ Exponentially small splitting of separatrices in a weakly hyperbolic case ⋮ Melnikov method and exponentially small splitting of separatrices

Cites Work

• Splitting of separatrices for the Chirikov standard map
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• The separation of motions in systems with rapidly rotating phase
• An asymptotic expression for the splitting of separatrices of the rapidly forced pendulum
• Beyond all orders: Singular perturbations in a mapping
• Splitting of separatrices for standard and semistandard mappings
• Rapidly forced planar vector fields and splitting of separatrices
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