Generalized results on the role of new-time transformations in finite-dimensional Poisson systems

TL;DR

This paper completely characterizes all new-time transformations that preserve the Poisson structure in finite-dimensional systems, generalizing previous results and providing concrete examples.

Contribution

It offers a complete, constructive characterization of all structure-preserving new-time transformations in finite-dimensional Poisson systems, expanding prior knowledge.

Findings

Complete classification of structure-preserving transformations

Generalization of known results in Poisson systems

Examples illustrating the theoretical findings

Abstract

The problem of characterizing all new-time transformations preserving the Poisson structure of a finitedimensional Poisson system is completely solved in a constructive way. As a corollary, this leads to a broad generalization of previously known results. Examples are given.