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A Geometric Approach to the Sundman Transformation and Its Applications to Integrability.
- Source :
-
Symmetry (20738994) . May2024, Vol. 16 Issue 5, p568. 27p. - Publication Year :
- 2024
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 16
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Symmetry (20738994)
- Publication Type :
- Academic Journal
- Accession number :
- 177490488
- Full Text :
- https://doi.org/10.3390/sym16050568