\(N\)-pulse homoclinic orbits in perturbations of resonant Hamiltonian systems
type: Item
instance of: scholarly article
title: \(N\)-pulse homoclinic orbits in perturbations of resonant Hamiltonian systems
zbMATH Open document ID: 0829.58016
DOI: 10.1007/BF00375655
author: Stephen Wiggins
author: G. Haller
published in: Archive for Rational Mechanics and Analysis
publication date: 1995-07-18T00:00:00Z
review text: The authors develop an analytical method to detect orbits doubly asymptotic to show manifolds in perturbations of integrable, two degree of freedom resonant Hamiltonian systems. The energy-phase method applies to both Hamiltonian and dissipative perturbations and reveals families of multi-pulse solutions which are not amenable to Melnikov-type methods. As an example, the authors study a two-mode approximation of the nonlinear, nonplanar oscillations of a parametrically forced inextensional beam. In this problem the authors find unusually complicated mechanisms for chaotic motions and verify their existence numerically.
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 775514
zbMATH Keywords: energy-phase method
zbMATH Keywords: resonant Hamiltonian systems
reviewed by: Yoshihide Kozai
MaRDI profile type: Publication
cites work: Existence and stability of asymptotically oscillatory triple pulses
cites work: Q4167627
cites work: Bifurcations of mode equations: Spin waves
cites work: Bifurcation of a plethora of multi-modal homoclinic orbits for autonomous Hamiltonian systems
cites work: Homoclinic bifurcation at resonant eigenvalues
cites work: Double Impulse Solutions in Nerve Axon Equations
cites work: Symmetry-breaking bifurcations in resonant surface waves
cites work: Global bifurcation and chaos in parametrically forced systems with one-one resonance
cites work: On the existence of chaos in a class of two-degree-of-freedom, damped, strongly parametrically forced mechanical systems with broken \(O(2)\) symmetry
cites work: Q5658861
cites work: Geometric singular perturbation theory for ordinary differential equations
cites work: Subsidiary bifurcations near bifocal homoclinic orbits
cites work: Orbits homoclinic to resonances: The Hamiltonian case
cites work: Q4849845
cites work: Multi-pulse jumping orbits and homoclinic trees in a modal truncation of the damped-forced nonlinear Schrödinger equation
cites work: Single and Multiple Pulse Waves for the FitzHugh–Nagumo
cites work: Invariant manifolds
cites work: Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom
cites work: Chaotic motions in a weakly nonlinear model for surface waves
cites work: Tracking invariant manifolds with differential forms in singularly perturbed systems
cites work: Tracking Invariant Manifolds up to Exponentially Small Errors
cites work: Multi-bump orbits homoclinic to resonance bands
cites work: Bifurcations to \(N\)-homoclinic orbits and \(N\)-periodic orbits in vector fields
cites work: Homoclinic and heteroclinic bifurcations of Vector fields
cites work: Orbits homoclinic to resonances, with an applications to chaos in a model of the forced and damped sine-Gordon equation
cites work: Singular perturbation theory for homoclinic orbits in a class of near- integrable Hamiltonian systems
cites work: Q4880398
cites work: Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle- center
cites work: Stable and Random Motions in Dynamical Systems
cites work: Nonlinear non-planar parametric responses of an inextensional beam
cites work: Homoclinic tangles-classification and applications
cites work: A CONTRIBUTION TO THE PROBLEM OF THE STRUCTURE OF AN EXTENDED NEIGHBORHOOD OF A ROUGH EQUILIBRIUM STATE OF SADDLE-FOCUS TYPE
cites work: THE MECHANISM OF DESTRUCTION OF RESONANCE TORI OF HAMILTONIAN SYSTEMS
cites work: Global bifurcations and chaos. Analytical methods
cites work: Normally hyperbolic invariant manifolds in dynamical systems
cites work: Non-linear phenomena in forced vibrations of a nearly square plate: Antisymmetric case
description: scientific article; zbMATH DE number 775514