Weak K. A. M. solutions and minimizing orbits of twist maps
DOI10.1090/tran/9017zbMath1529.37031arXiv2209.11544OpenAlexW4297415683MaRDI QIDQ6051570
Marie-Claude Arnaud, Maxime Zavidovique
Publication date: 20 October 2023
Full work available at URL: https://arxiv.org/abs/2209.11544
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30) Dynamical aspects of twist maps (37E40) Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods (37J51) Symplectic and canonical mappings (37J11)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Convergence of the solutions of the discounted equation: the discrete case
- The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
- Ilmanen's Lemma on insertion of \(C^{1,1}\) functions
- Lasry-Lions regularization and a lemma of Ilmanen
- Existence of \(C^{1,1}\) critical subsolutions in discrete weak KAM theory
- Strict sub-solutions and Mañé potential in discrete weak KAM theory
- Semiconcave functions, Hamilton-Jacobi equations, and optimal control
- Action minimizing invariant measures for positive definite Lagrangian systems
- Three results on the regularity of the curves that are invariant by an exact symplectic twist map
- Geodesic rays, Busemann functions and monotone twist maps
- Order property and modulus of continuity of weak KAM solutions
- Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
- Connecting orbits of time dependent Lagrangian systems
- Global behaviors of weak KAM solutions for exact symplectic twist maps
- The Lax–Oleinik semi-group: a Hamiltonian point of view
- Pseudographs and the Lax–Oleinik semi-group: a geometric and dynamical interpretation
- Minimizing orbits in the discrete Aubry–Mather model
- The dynamics of pseudographs in convex Hamiltonian systems
- Monotone twist mappings and the calculus of variations
- Differentiability of the minimal average action as a function of the rotation number
- On the minimizing measures of Lagrangian dynamical systems
- Convergence of discrete Aubry–Mather model in the continuous limit
- Hyperbolicity for conservative twist maps of the 2-dimensional annulus
- Convergence of the semi-group of Lax–Oleinik: a geometric point of view
- Viscous stability of quasi-periodic tori
- Existence of C1,1C1,1 critical sub-solutions of the Hamilton–Jacobi equation on compact manifolds
- Actions of symplectic homeomorphisms/diffeomorphisms on foliations by curves in dimension 2
This page was built for publication: Weak K. A. M. solutions and minimizing orbits of twist maps
