Scaling symmetries and canonoid transformations in Hamiltonian systems

TL;DR

This paper explores various symmetries in Hamiltonian systems across different geometric structures, focusing on non-standard symmetries like scaling and canonoid transformations, and their relation to conserved quantities.

Contribution

It characterizes non-standard symmetries such as scaling and canonoid transformations in Hamiltonian systems on diverse geometric manifolds.

Findings

Characterization of non-standard symmetries in Hamiltonian systems

Analysis of the relationship between symmetries and conserved quantities

Extension of symmetry concepts to non-canonical transformations

Abstract

We investigate various types of symmetries and their mutual relationships in Hamiltonian systems defined on manifolds with different geometric structures: symplectic, cosymplectic, contact and cocontact. In each case we pay special attention to non-standard (non-canonical) symmetries, in particular scaling symmetries and canonoid transformations, as they provide new interesting tools for the qualitative study of these systems. Our main results are the characterizations of these non-standard symmetries and the analysis of their relation with conserved (or dissipated) quantities.