On locally conformally cosymplectic Hamiltonian dynamics and Hamilton–Jacobi theory

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 06 Jan 2023Embargo end date: 01 Jan 2022 Spain Publisher:IOP PublishingJournal:Journal of Physics A: Mathematical and Theoretical, volume 56, page 15,204 (issn: 1751-8113, eissn: 1751-8121,

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Authors: Begüm Ateşli; Oğul Esen; Manuel de León; Cristina Sardón;

doi: 10.1088/1751-8121/acafb2 , 10.48550/arxiv.2205.13329

arXiv: 2205.13329

handle: 10261/347056

On locally conformally cosymplectic Hamiltonian dynamics and Hamilton–Jacobi theory

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Abstract

Abstract Cosymplectic geometry has been proven to be a very useful geometric background to describe time-dependent Hamiltonian dynamics. In this work, we address the globalization problem of locally cosymplectic Hamiltonian dynamics that failed to be globally defined. We investigate both the geometry of locally conformally cosymplectic (LCC) manifolds and the Hamiltonian dynamics constructed on such LCC manifolds. Further, we provide a geometric Hamilton–Jacobi theory on this geometric framework.

Country

Spain

Related Organizations

Gebze Technical University
Turkey
Institute of Mathematical Sciences
Spain
Universidad Politécnica de Madrid
Spain
Spanish National Research Council
Spain

Keywords

Mathematics - Differential Geometry, Darboux theorem, Geometric Hamilton Jacobi theory, Hamilton-Jacobi equations in mechanics, Hamiltonian dynamics, geometric Hamilton-Jacobi theory, time-dependent Hamiltonian dynamics, Locally conformally cosymplectic, Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics, line bundle, Differential Geometry (math.DG), FOS: Mathematics, Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics, Lie algebroid

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