On Non-autonomous Hamiltonian Dynamics, Dual Spaces, and Kinetic Lifts
Differential Geometry
2023-08-22 v1 Mathematical Physics
math.MP
Abstract
Vlasov kinetic theory is the dynamics of a bunch of particles flowing according to symplectic Hamiltonian dynamics. More recently, this geometry has been extended to contact Hamiltonian dynamics. In this paper, we introduce geometric kinetic theories within the framework of cosymplectic and cocontact manifolds to extend the present literature to time-dependent dynamics. The cosymplectic and the cocontact kinetic theories are obtained in terms of both momentum variables and density functions. These alternative realizations are linked via Poisson/momentum maps. Furthermore, in cocontact geometry, we introduce a hierarchical analysis of nine distinct dynamical motions as various manifestations of Hamiltonian, evolution, and gradient flows.
Keywords
Cite
@article{arxiv.2308.10336,
title = {On Non-autonomous Hamiltonian Dynamics, Dual Spaces, and Kinetic Lifts},
author = {Begüm Ateşli and Oğul Esen and Manuel de León and Cristina Sardón},
journal= {arXiv preprint arXiv:2308.10336},
year = {2023}
}