Geometry and chaos near resonant equilibria of 3-DOF Hamiltonian systems
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Publication:1906096
DOI10.1016/0167-2789(95)00247-2zbMath0894.70014OpenAlexW2108203555MaRDI QIDQ1906096
Stephen Wiggins, György Haller
Publication date: 6 February 1996
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0167-2789(95)00247-2
heteroclinic connectionshomoclinic connectionsexistence of families of 3-tori and whiskered 2-toriinvariant 3-sphereslocal normal formquartic normal form
Bifurcations and instability for nonlinear problems in mechanics (70K50) Hamilton's equations (70H05) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)
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Cites Work
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- Lagrangian submanifolds and Hamiltonian systems
- Long periodic orbits near an equilibrium and the averaging method in higher-order resonances
- Chaos in the 1:2:3 Hamiltonian normal form
- On resonant classical Hamiltonians with n frequencies
- Reduction of the semisimple \(1:1\) resonance
- Estimates in the Kolmogorov theorem on conservation of conditionally periodic motions
- Invariant manifolds and the initialization problem for some atmospheric equations
- Stability of motions near resonances in quasi-integrable Hamiltonian systems
- On elliptic lower dimensional tori in Hamiltonian systems
- On averaging, reduction, and symmetry in Hamiltonian systems
- Geometric singular perturbation theory for ordinary differential equations
- Global bifurcations and chaos. Analytical methods
- Multiphase averaging for classical systems. With applications to adiabatic theorems. Transl. from the French by H. S. Dumas
- Hamiltonian and Lagrangian flows on center manifolds with applications to elliptic variational problems
- An asymptotic expression for the splitting of separatrices of the rapidly forced pendulum
- An interaction of three resonant modes in a nonlinear lattice
- Tracking invariant manifolds with differential forms in singularly perturbed systems
- Normally hyperbolic invariant manifolds in dynamical systems
- Normal forms for three-dimensional parametric instabilities in ideal hydrodynamics
- \(N\)-pulse homoclinic orbits in perturbations of resonant Hamiltonian systems
- Geometry and chaos near resonant equilibria of 3-DOF Hamiltonian systems
- Transcendentally small transversality in the rapidly forced pendulum
- Convergent series expansions for quasi-periodic motions
- On the conservation of hyperbolic invariant tori for Hamiltonian systems
- Normal modes for nonlinear Hamiltonian systems
- Stable and Random Motions in Dynamical Systems
- Asymptotic Integrability and Periodic Solutions of a Hamiltonian System in $1:2:2$-Resonance
- Non-integrability of the 1:1:2–resonance
- First-order resonances in three-degrees-of-freedom systems
- Stability of nonlinear normal modes of symmetric Hamiltonian systems
- Existence of nonlinear normal modes of symmetric Hamiltonian systems
- Homoclinic and heteroclinic orbits of reversible vectorfields under perturbation
- On the number of isolating integrals in resonant systems with 3 degrees of freedom
- Melnikov’s method and Arnold diffusion for perturbations of integrable Hamiltonian systems
- Generalized implicit function theorems with applications to some small divisor problems, II
- AN EXPONENTIAL ESTIMATE OF THE TIME OF STABILITY OF NEARLY-INTEGRABLE HAMILTONIAN SYSTEMS
- Complex analysis and convolution operators
- Multi-bump orbits homoclinic to resonance bands
- SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS
- Averaging methods in nonlinear dynamical systems