Stability islands in the vicinity of separatrices of near-integrable symplectic maps

DOI10.3934/dcdsb.2008.10.681zbMath1153.37406OpenAlexW2313242226MaRDI QIDQ950610

Carles Simó, Dmitrij V. Treshev

Publication date: 30 October 2008

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2008.10.681

zbMATH Keywords

area preserving mapsstability islandsseparatrix mapslobes defined by invariant manifold

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics (70K44) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items

Invariant manifolds at infinity of the RTBP and the boundaries of bounded motion, Return maps, dynamical consequences and applications, Dynamics in chaotic zones of area preserving maps: close to separatrix and global instability zones, From the Hénon conservative map to the Chirikov standard map for large parameter values, Some remarks on the abundance of stable periodic orbits inside homoclinic lobes, Measuring the total amount of chaos in some Hamiltonian systems, The parametrically forced pendulum: A case study in \(1\frac12\) degree of freedom, Effective bounds for the measure of rotations