On a theorem by Mather and Aubry-Mather sets for planar Hamiltonian systems

DOI10.1007/BF02875979zbMath0976.70014MaRDI QIDQ1974190

Mei Yue Jiang

Publication date: 28 August 2000

Published in: Science in China. Series A (Search for Journal in Brave)

zbMATH Keywords

Legendre transformationminimal solutionssymplectic coordinatesplane Hamiltonian systemexistence of Aubry-Mather setsMather's theoremsuperlinear positive definite Lagrangian systems

Mathematics Subject Classification ID

Hamilton's equations (70H05) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Dynamical systems in classical and celestial mechanics (37N05) Lagrange's equations (70H03) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items (3)

Periodic solutions of second order differential equations with discontinuous nonlinearities ⋮ Subharmonic solutions of second order subquadratic Hamiltonian systems with potential changing sign ⋮ Quasiperiodic dynamics in Hamiltonian \(1\frac{1}{2}\) degree of freedom systems far from integrability

Cites Work

• Unnamed Item
• The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
• Mather sets for superlinear Duffing equations
• Action minimizing invariant measures for positive definite Lagrangian systems
• Mather sets for plane Hamiltonian systems
• Aubry-Mather sets for finite-twist maps of a cylinder and semilinear Duffing equations
• Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
• Recent Developments in the Theory of Hamiltonian Systems

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