Construction of invariant whiskered tori by a parameterization method. II: Quasi-periodic and almost periodic breathers in coupled map lattices

DOI10.1016/j.jde.2015.03.034zbMath1351.37258arXiv1406.1091OpenAlexW2005003952MaRDI QIDQ2347814

Yannick Sire, Rafael de la Llave, Ernest Fontich

Publication date: 9 June 2015

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.1091

zbMATH Keywords

Nash-Moser iterationinvariant torusinfinite latticehyperbolic fixed pointcoupled Hamiltonian systems

Mathematics Subject Classification ID

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) Dynamical systems with hyperbolic orbits and sets (37D05) Lattice dynamics; integrable lattice equations (37K60) Nearly integrable Hamiltonian systems, KAM theory (70H08) PDEs in connection with mechanics of particles and systems of particles (35Q70)

Related Items (13)

Whiskered KAM tori of conformally symplectic systems ⋮ Quasi-periodic solution for the complex Ginzburg-Landau equation with continuous spectrum ⋮ Response solution to ill-posed Boussinesq equation with quasi-periodic forcing of Liouvillean frequency ⋮ Breathers as metastable states for the discrete NLS equation ⋮ An a posteriori KAM theorem for whiskered tori in Hamiltonian partial differential equations with applications to some ill-posed equations ⋮ Localized stable manifolds for whiskered tori in coupled map lattices with decaying interaction ⋮ Normal forms and Sternberg conjugation theorems for infinite dimensional coupled map lattices ⋮ Periodic motions for FPU lattice systems with asymptotically quadratic potentials ⋮ Some breathers and multi-breathers for FPU-type chains ⋮ Existence of whiskered KAM tori of conformally symplectic systems ⋮ Invariant manifolds of parabolic fixed points. I: Existence and dependence on parameters ⋮ Construction of invariant whiskered tori by a parameterization method. I: Maps and flows in finite dimensions ⋮ Construction of quasi-periodic solutions of delay differential equations via KAM techniques

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dynamical systems on lattices with decaying interaction. I: A functional analysis framework
• Dynamical systems on lattices with decaying interaction. II: Hyperbolic sets and their invariant manifolds
• Travelling breathers in Klein-Gordon lattices as homoclinic orbits to \(p\)-tori
• Existence and stability of quasi-periodic breathers in networks of Ginzburg--Landau oscillators
• Small divisors with spatial structure in infinite dimensional Hamiltonian systems
• Quasi-periodic breathers in Hamiltonian networks of long-range coupling
• Construction of invariant whiskered tori by a parameterization method. I: Maps and flows in finite dimensions
• Localization in disordered, nonlinear dynamical systems
• Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations
• Localized breather-like solution in a discrete Klein-Gordon model and application to DNA
• Moser's implicit function theorem in the framework of analytic smoothing
• Properties of infinite dimensional Hamiltonian systems
• Hyperbolic tori and asymptotic surfaces in Hamiltonian systems
• Perturbations of lower dimensional tori for Hamiltonian systems
• Robustness of exponential dichotomies in infinite-dimensional dynamical systems
• Existence theorem for solitary waves on lattices
• Second order Hamiltonian equations on \(\mathbb{T}^ \infty\) and almost- periodic solutions
• Construction of quasi-periodic breathers via KAM technique
• Multibump periodic motions of an infinite lattice of particles
• Travelling waves in a chain of coupled nonlinear oscillators
• Smooth dependence of thermodynamic limits of SRB-measures
• Quasiperiodic breathers in Hamiltonian lattices with symmetries
• Plenty of elliptic islands for the standard family of area preserving maps
• A method for the study of whiskered quasi-periodic and almost-periodic solutions in finite and infinite dimensional Hamiltonian systems
• Localized stable manifolds for whiskered tori in coupled map lattices with decaying interaction
• A KAM theorem for reversible systems of infinite dimension
• Global attraction to solitary waves in models based on the Klein-Gordon equation
• The Fermi-Pasta-Ulam problem. A status report
• Dynamics of coupled map lattices and of related spatially extended systems. Lectures delivered at the school-forum CML 2004, Paris, France, June 21 -- July 2, 2004.
• Convergent series expansions for quasi-periodic motions
• Neighborhoods of hyperbolic sets
• On the conservation of hyperbolic invariant tori for Hamiltonian systems
• Travelling breathers with exponentially small tails in a chain of nonlinear oscillators
• On global attraction to solitary waves for the Klein-Gordon field coupled to several nonlinear oscillators
• Existence of breathers on FPU lattices
• VIRIAL RELATIONS FOR NONLINEAR WAVE EQUATIONS AND NONEXISTENCE OF ALMOST PERIODIC SOLUTIONS
• Solitary waves on FPU lattices: II. Linear implies nonlinear stability
• Elliptic isles in families of area-preserving maps
• Generalized implicit function theorems with applications to some small divisor problems, I
• Generalized implicit function theorems with applications to some small divisor problems, II
• On optimal estimates for the solutions of linear difference equations on the circle
• On a new proof of Moser's twist mapping theorem
• On the Darboux theorem for weak symplectic manifolds
• Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators
• Solitary waves on Fermi–Pasta–Ulam lattices: III. Howland-type Floquet theory
• Solitary waves on Fermi–Pasta–Ulam lattices: IV. Proof of stability at low energy
• Travelling waves in the Fermi-Pasta-Ulam lattice
• KAM theory without action-angle variables
• Solitary waves on FPU lattices: I. Qualitative properties, renormalization and continuum limit
• Coupled maps and analytic function spaces
• Nonlinear dynamics and statistical physics of DNA
• Coupled analytic maps
• Periodic motions of an infinite lattice of particles with nearest neighbor interaction
• A KAM theorem for Hamiltonian networks with long ranged couplings
• Invariant manifolds
• Variational proof for hard discrete breathers in some classes of Hamiltonian dynamical systems.

This page was built for publication: Construction of invariant whiskered tori by a parameterization method. II: Quasi-periodic and almost periodic breathers in coupled map lattices