Liouville’s theorem and the canonical measure for nonconservative systems from contact geometry

DOI10.1088/1751-8113/48/24/245001zbMath1321.37067arXiv1412.0026OpenAlexW1546462952MaRDI QIDQ5261649

Diego Tapias, Alessandro Bravetti

Publication date: 6 July 2015

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.0026

zbMATH Keywords

invariant measurecontact geometrynon-Hamiltonian dynamics

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Classical equilibrium statistical mechanics (general) (82B05)

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Contact Hamiltonian mechanics ⋮ Herglotz action for homogeneous cosmologies ⋮ Covariant statistical mechanics of non-Hamiltonian systems ⋮ Exact Baker–Campbell–Hausdorff formula for the contact Heisenberg algebra ⋮ Contact Hamiltonian Systems for Probability Distribution Functions and Expectation Variables: A Study Based on a Class of Master Equations ⋮ Scalar fields and the FLRW singularity ⋮ Contact symmetries and Hamiltonian thermodynamics ⋮ Thermodynamics and evolutionary biology through optimal control ⋮ Contact Hamiltonian systems ⋮ The Lagrange-Charpit theory of the Hamilton-Jacobi problem ⋮ Contact geometric descriptions of vector fields on dually flat spaces and their applications in electric circuit models and nonequilibrium statistical mechanics ⋮ Legendre submanifolds in contact manifolds as attractors and geometric nonequilibrium thermodynamics ⋮ Invariant measures for contact Hamiltonian systems: symplectic sandwiches with contact bread

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