Ghost circles in lattice Aubry-Mather theory

DOI10.1016/J.JDE.2011.11.023zbMath1253.37062arXiv1111.5963OpenAlexW2155105548MaRDI QIDQ665981

Bob Rink, Blaž Mramor

Publication date: 7 March 2012

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

Full work available at URL: https://arxiv.org/abs/1111.5963

zbMATH Keywords

gaprotation vectorAubry-Mather setFrenkel-Kontorova problemghost circlelattice reccurence relations

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Lattice dynamics; integrable lattice equations (37K60)

Related Items (15)

An example for nonexistence of minimal foliations ⋮ A chaotic lattice field theory in one dimension* ⋮ Mountain pass solutions to a generalized Frenkel-Kontorova model ⋮ Depinning transition of travelling waves for particle chains ⋮ Continuity of depinning force ⋮ Pseudo solutions, rotation sets, and shadowing rotations for monotone recurrence relations ⋮ Positive topological entropy for monotone recurrence relations ⋮ Secondary invariants of Birkhoff minimizers and heteroclinic orbits ⋮ Minimal foliations for the high-dimensional Frenkel-Kontorova model ⋮ Multitransition solutions for a generalized Frenkel-Kontorova model ⋮ Invariant circles and depinning transition ⋮ A Necessary Condition of Nonminimal Aubry–Mather Sets for Monotone Recurrence Relations ⋮ A dichotomy theorem for minimizers of monotone recurrence relations ⋮ Heteroclinic solutions for a generalized Frenkel-Kontorova model by minimization methods of Rabinowitz and Stredulinsky ⋮ Continuity of the Peierls barrier and robustness of laminations

Cites Work

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• Converse KAM: theory and practice
• Minimal solutions of variational problems on a torus
• A uniqueness theorem for \(Z^ n\)-periodic variational problems
• The periodic orbits of an area preserving twist map
• Ghost circles for twist maps
• A new proof of the Aubry-Mather's theorem
• Aubry-Mather theory for functions on lattices
• Critical points inside the gaps of ground state laminations for some models in statistical mechanics
• Metric properties of minimal solutions of discrete periodical variational problems
• Differential Topology
• Ground states and critical points for Aubry-Mather theory in Statistical mechanics

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