A Geometric Approach to the Sundman Transformation and Its Applications to Integrability

Autor: José F. Cariñena
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: Symmetry, Vol 16, Iss 5, p 568 (2024)
Druh dokumentu: article
ISSN: 16050568
2073-8994
DOI: 10.3390/sym16050568
Popis: A geometric approach to the integrability and reduction of dynamical systems, both when dealing with systems of differential equations and in classical physics, is developed from a modern perspective. The main ingredients of this analysis are infinitesimal symmetries and tensor fields that are invariant under the given dynamics. A particular emphasis is placed on the existence of alternative invariant volume forms and the associated Jacobi multiplier theory, and then the Hojman symmetry theory is developed as a complement to the Noether theorem and non-Noether constants of motion. We also recall the geometric approach to Sundman infinitesimal time-reparametrisation for autonomous systems of first-order differential equations and some of its applications to integrability, and an analysis of how to define Sundman transformations for autonomous systems of second-order differential equations is proposed, which shows the necessity of considering alternative tangent bundle structures. A short description of alternative tangent structures is provided, and an application to integrability, namely, the linearisability of scalar second-order differential equations under generalised Sundman transformations, is developed.
Databáze: Directory of Open Access Journals
Externí odkaz:
Nepřihlášeným uživatelům se plný text nezobrazuje