Homoclinic orbits with many loops near a \(0^2 i\omega\) resonant fixed point of Hamiltonian systems

DOI10.3934/dcds.2016.36.3153zbMath1354.37060arXiv1401.1509OpenAlexW3101805048MaRDI QIDQ255913

Patrick Bernard, Eric Lombardi, Tiphaine Jézéquel

Publication date: 9 March 2016

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

Full work available at URL: https://arxiv.org/abs/1401.1509

zbMATH Keywords

invariant manifoldsHamiltonian systemsnormal formsexponentially small phenomenahomoclinic orbits with several loopsKAM

Mathematics Subject Classification ID

Related Items (6)

Breakdown of a 2D heteroclinic connection in the Hopf-zero singularity. I ⋮ On the existence of homoclinic orbits in \(n\)-dimensional piecewise affine systems ⋮ Quasi-periodic Hamiltonian pitchfork bifurcation in a phenomenological model with 3 degrees of freedom ⋮ The 0:1 resonance bifurcation associated with the supercritical Hamiltonian pitchfork bifurcation ⋮ Hopf-zero singularities truly unfold chaos ⋮ Dynamics of Klein-Gordon on a compact surface near a homoclinic orbit

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