The Aubry set and Mather set in the embedded contact Hamiltonian system
DOI10.1007/s10114-022-0531-xzbMath1502.37065OpenAlexW4285807472WikidataQ114228362 ScholiaQ114228362MaRDI QIDQ2157580
Publication date: 22 July 2022
Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10114-022-0531-x
Symplectic manifolds (general theory) (53D05) Contact manifolds (general theory) (53D10) Contact systems (37J55) Symplectic and canonical mappings (37J11) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)
Cites Work
- Weak KAM theory for Hamilton-Jacobi equations depending on unknown functions
- Action minimizing invariant measures for positive definite Lagrangian systems
- Variational construction of connecting orbits
- Symplectic invariants of elliptic fixed points
- Variational principle for contact Hamiltonian systems and its applications
- Aubry-Mather theory for contact Hamiltonian systems
- The principle of least action in geometry and dynamics
- Herglotz' generalized variational principle and contact type Hamilton-Jacobi equations
- Long-time asymptotic solutions of convex Hamilton-Jacobi equations depending on unknown functions
- Aubry-Mather theory for conformally symplectic systems
- Contact Hamiltonian mechanics
- Implicit variational principle for contact Hamiltonian systems
- Lagrangian flows: The dynamics of globally minimizing orbits
- Lagrangian flows: The dynamics of globally minimizing orbits-II
- The action spectrum near positive definite invariant tori
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