Minimal measures beyond Mather

DOI10.1007/S00526-024-02759-9MaRDI QIDQ6564431

Min Zhou

Publication date: 1 July 2024

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

zbMATH Keywords

minimal measureMañé critical valuefirst cohomology classfirst homology class

Mathematics Subject Classification ID

Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods (37J51) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Cites Work

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• Smooth linearization of hyperbolic fixed points without resonance conditions
• Homoclinic orbits of positive definite Lagrangian systems
• Action minimizing invariant measures for positive definite Lagrangian systems
• Variational construction of connecting orbits
• Connecting orbits between static classes for generic Lagrangian systems
• Minimal measures on the level sets below Mañé critical value
• A generic property of families of Lagrangian systems
• Generic properties and problems of minimizing measures of Lagrangian systems
• On minimizing measures of the action of autonomous Lagrangians

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