Aubry-Mather theory for functions on lattices

DOI10.3934/dcds.1997.3.135zbMath0948.37015OpenAlexW2033543882MaRDI QIDQ1576712

Rafael de la Llave, Hans Koch, Charles Radin

Publication date: 16 August 2000

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.1997.3.135

zbMATH Keywords

quasi-periodic solutionsAubry-Mather theorem

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Periodic and quasi-periodic flows and diffeomorphisms (37C55) Lattice dynamics; integrable lattice equations (37K60)

Related Items (17)

Symplectic twist maps without conjugate points ⋮ An example for nonexistence of minimal foliations ⋮ Multiplicity results for interfaces of Ginzburg-Landau-Allen-Cahn equations in periodic media ⋮ Depinning transition of travelling waves for particle chains ⋮ Minimal configurations for the Frenkel-Kontorova model on a quasicrystal ⋮ Continuity of depinning force ⋮ Pseudo solutions, rotation sets, and shadowing rotations for monotone recurrence relations ⋮ A continuous family of equilibria in ferromagnetic media are ground states ⋮ Secondary invariants of Birkhoff minimizers and heteroclinic orbits ⋮ Minimal foliations for the high-dimensional Frenkel-Kontorova model ⋮ Percival Lagrangian approach to the Aubry-Mather theory ⋮ Minimisers of the Allen-Cahn equation and the asymptotic plateau problem on hyperbolic groups ⋮ Ghost circles in lattice Aubry-Mather theory ⋮ Critical points inside the gaps of ground state laminations for some models in statistical mechanics ⋮ Minimisers of the Allen-Cahn equation on hyperbolic graphs ⋮ A generalization of Aubry-Mather theory to partial differential equations and pseudo-differential equations ⋮ Ground states and critical points for Aubry-Mather theory in Statistical mechanics

This page was built for publication: Aubry-Mather theory for functions on lattices