A new proof of the Aubry-Mather's theorem

DOI10.1007/BF02571806zbMath0759.58039MaRDI QIDQ1204276

Christophe Golé

Publication date: 3 March 1993

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174411

zbMATH Keywords

Aubry-Mather setstwist mapsexistence of quasi periodic orbits

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Periodic and quasi-periodic flows and diffeomorphisms (37C55)

Related Items (11)

Minimal foliations for the high-dimensional Frenkel-Kontorova model ⋮ Existence and modulation of uniform sliding states in driven and overdamped particle chains ⋮ Denjoy minimal sets and Birkhoff periodic orbits for non-exact monotone twist maps ⋮ Aubry-Mather theory and the inverse spectral problem for planar convex domains ⋮ Slope-changing solutions of elliptic problems on \(\mathbb R^n\) ⋮ Ghost circles in lattice Aubry-Mather theory ⋮ Invariant circles and depinning transition ⋮ Many Solutions of Elliptic Problems on Rⁿof Irrational Slope ⋮ A Necessary Condition of Nonminimal Aubry–Mather Sets for Monotone Recurrence Relations ⋮ 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

Cites Work

• The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
• The periodic orbits of an area preserving twist map
• Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
• Monotone recurrence relations, their Birkhoff orbits and topological entropy

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