On the continuation of degenerate periodic orbits via normal form: lower dimensional resonant tori
From MaRDI portal
Publication:2208170
DOI10.1016/j.cnsns.2020.105360zbMath1453.37059arXiv2005.11859OpenAlexW2760299103MaRDI QIDQ2208170
Tiziano Penati, Veronica Danesi, Simone Paleari, Marco Sansottera
Publication date: 23 October 2020
Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.11859
Quasi-periodic motions and invariant tori for nonlinear problems in mechanics (70K43) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Nearly integrable Hamiltonian systems, KAM theory (70H08)
Related Items
Low dimensional completely resonant tori in Hamiltonian lattices and a theorem of Poincaré, Stationary solutions of discrete Landau-de Gennes theory: \(3 \times 3\) Q-tensor case, Kolmogorov variation: Kam with knobs \textit{(à la Kolmogorov)}, Continuation of spatially localized periodic solutions in discrete NLS lattices via normal forms
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Non-existence of phase-shift breathers in one-dimensional Klein-Gordon lattices with nearest-neighbor interactions
- On the convergence of an algorithm constructing the normal form for elliptic lower dimensional tori in planetary systems
- Lower-dimensional tori in multi-scale, nearly integrable Hamiltonian systems
- Invariant tori in Hamiltonian systems with high order proper degeneracy
- On the continuation of degenerate periodic orbits in Hamiltonian systems
- The discrete nonlinear Schrödinger equation. Mathematical analysis, numerical computations and physical perspectives
- Breathers in nonlinear lattices: existence, linear stability and quantization
- Introduction to Hamiltonian dynamical systems and the \(N\)-body problem.
- The surviving of lower dimensional tori from a resonant torus of Hamiltonian systems
- Kolmogorov theorem and classical perturbation theory
- A quasi-periodic Poincaré's theorem
- On the nonexistence of degenerate phase-shift discrete solitons in a dNLS nonlocal lattice
- Rigorous estimates for the relegation algorithm
- Poincaré-Treshchev mechanism in multi-scale, nearly integrable Hamiltonian systems
- Dynamics of breathers in discrete nonlinear Schrödinger models
- Stability of discrete breathers
- Multibreathers in Klein-Gordon chains with interactions beyond nearest neighbors
- On the continuation of degenerate periodic orbits via normal form: full dimensional resonant tori
- Normalization of a periodic Hamiltonian system
- On the nonexistence of degenerate phase-shift multibreathers in Klein-Gordon models with interactions beyond nearest neighbors
- Variational approximations in discrete nonlinear Schrödinger equations with next-nearest-neighbor couplings
- Hamiltonian lattice dynamics
- Improved convergence estimates for the Schröder-Siegel problem
- A semi-analytic algorithm for constructing lower dimensional elliptic tori in planetary systems
- Degenerate lower-dimensional tori in Hamiltonian systems
- On the conservation of hyperbolic invariant tori for Hamiltonian systems
- Stability of discrete solitons in nonlinear Schrödinger lattices
- Persistence and stability of discrete vortices in nonlinear Schrödinger lattices
- MULTIBREATHER AND VORTEX BREATHER STABILITY IN KLEIN–GORDON LATTICES: EQUIVALENCE BETWEEN TWO DIFFERENT APPROACHES
- On the stability of multibreathers in Klein–Gordon chains
- THE MECHANISM OF DESTRUCTION OF RESONANCE TORI OF HAMILTONIAN SYSTEMS
- Multi-site breathers in Klein–Gordon lattices: stability, resonances and bifurcations
- Differential Dynamical Systems, Revised Edition
- DEGENERATE BIFURCATIONS OF RESONANT TORI IN HAMILTONIAN SYSTEMS
- Stability of waves in perturbed Hamiltonian systems
- Dynamics of relative phases: generalised multibreathers
