Separatrices splitting for Birkhoff’s billiard in symmetric convex domain, closed to an ellipse
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Publication:4526314
DOI10.1063/1.166037zbMath1055.37551OpenAlexW2035041399WikidataQ52362970 ScholiaQ52362970MaRDI QIDQ4526314
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Publication date: 16 January 2001
Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.166037
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Cites Work
- Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom
- The existence of an infinite number of elliptic and hyperbolic periodic trajectories for a convex billiard
- Splitting of separatrices for standard and semistandard mappings
- The analytic invariants of an area-preserving mapping near a hyperbolic fixed point
- Local Contractions and a Theorem of Poincare
- Computing the dependence on a parameter of a family of unstable manifolds: generalized Melnikov formulas
- Horseshoes for autonomous Hamiltonian systems using the Melnikov integral
- Melnikov’s method and Arnold diffusion for perturbations of integrable Hamiltonian systems
- Mel’nikov’s Function for Two-Dimensional Mappings
- Exponentially small splittings in Hamiltonian systems
- QUASIRANDOM DYNAMICAL SYSTEMS. III QUASIRANDOM OSCILLATIONS OF ONE-DIMENSIONAL OSCILLATORS