Invariant circles and depinning transition

DOI10.1017/etds.2016.42zbMath1390.37075OpenAlexW2522559858MaRDI QIDQ4643263

Wen-Xin Qin, Ya-Nan Wang

Publication date: 24 May 2018

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/etds.2016.42

zbMATH Keywords

Frenkel-Kontorova modelarea-preserving twist maprotational invariant circle

Mathematics Subject Classification ID

Related Items (6)

Resonant equilibrium configurations in quasi-periodic media: perturbative expansions ⋮ Depinning transition of travelling waves for particle chains ⋮ Continuity of depinning force ⋮ Decomposing dynamics via components of rotation sets ⋮ Minimal foliations for the high-dimensional Frenkel-Kontorova model ⋮ Denjoy minimal sets and Birkhoff periodic orbits for non-exact monotone twist maps

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
• A nondifferentiable essential irrational invariant curve for a \(C^1\) symplectic twist map
• Ghost circles in lattice Aubry-Mather theory
• Scaling exponents at the transition by breaking of analyticity for incommensurate structures
• Converse KAM: theory and practice
• A criterion for the non-existence of invariant circles
• The periodic orbits of an area preserving twist map
• Ghost circles for twist maps
• A new proof of the Aubry-Mather's theorem
• Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
• Existence of dynamical hull functions with two variables for the ac-driven Frenkel-Kontorova model
• Multiplicity results for interfaces of Ginzburg-Landau-Allen-Cahn equations in periodic media
• Existence and modulation of uniform sliding states in driven and overdamped particle chains
• Critical points inside the gaps of ground state laminations for some models in statistical mechanics
• On the necessity of gaps
• Mañé's conjectures in codimension 1
• Stable and Random Motions in Dynamical Systems
• Dynamics of the Frenkel–Kontorova model with irrational mean spacing
• Symplectic maps, variational principles, and transport
• Recent Developments in the Theory of Hamiltonian Systems
• Gradient dynamics of tilted Frenkel-Kontorova models
• Existence and modulation of traveling waves in particles chains
• Décomposition des difféomorphismes du tore en applications déviant la verticale (avec un appendice en collaboration avec Jean-Marc Gambaudo)
• A numerically accessible criterion for the breakdown of quasi-periodic solutions and its rigorous justification
• Continuity of the Peierls barrier and robustness of laminations
• Many Solutions of Elliptic Problems on Rⁿof Irrational Slope
• Ground states and critical points for Aubry-Mather theory in Statistical mechanics

This page was built for publication: Invariant circles and depinning transition