Unimodularity and invariant volume forms for Hamiltonian dynamics on coisotropic Poisson homogeneous spaces

TL;DR

This paper introduces the concept of multiplicative unimodularity for coisotropic Poisson homogeneous spaces, explores conditions for invariant volume forms in Hamiltonian systems, and provides illustrative examples.

Contribution

It defines multiplicative unimodularity for these spaces and analyzes the existence of invariant volume forms in Hamiltonian dynamics.

Findings

Defined multiplicative unimodularity for coisotropic Poisson homogeneous spaces

Established conditions for invariant volume forms in Hamiltonian systems

Presented examples illustrating theoretical results

Abstract

In this paper, we introduce the notion of a multiplicative unimodularity for a coisotropic Poisson homogeneous space. Then, we discuss the unimodularity and the multiplicative unimodularity for these spaces and the existence of an invariant volume form for explicit Hamiltonian systems on such spaces. Several interesting examples illustrating the theoretical results are also presented.