Continuity of the Peierls barrier and robustness of laminations

DOI10.1017/etds.2013.101zbMath1364.37135arXiv1308.3073OpenAlexW3104733013MaRDI QIDQ5262264

Bob Rink, Blaž Mramor

Publication date: 13 July 2015

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

Full work available at URL: https://arxiv.org/abs/1308.3073

zbMATH Keywords

variational methodAubry-Mather theoryquasi-periodicsmall divisor

Mathematics Subject Classification ID

Related Items (3)

Continuity of depinning force ⋮ Minimal foliations for the high-dimensional Frenkel-Kontorova model ⋮ Invariant circles and depinning transition

Cites Work

• The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
• Ghost circles in lattice Aubry-Mather theory
• Converse KAM: theory and practice
• A uniqueness theorem for \(Z^ n\)-periodic variational problems
• Equivalence of uniform hyperbolicity for symplectic twist maps and phonon gap for Frenkel-Kontorova models
• KAM theory in configuration space
• Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
• Critical points inside the gaps of ground state laminations for some models in statistical mechanics
• Monotone recurrence relations, their Birkhoff orbits and topological entropy
• Quasi-periodic solutions of nonlinear elliptic partial differential equations
• Analytic destruction of invariant circles
• A numerically accessible criterion for the breakdown of quasi-periodic solutions and its rigorous justification
• Ground states and critical points for Aubry-Mather theory in Statistical mechanics

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