The dynamics of conformal Hamiltonian flows: dissipativity and conservativity

TL;DR

This paper investigates the complex behaviors of conformal Hamiltonian flows on conformal symplectic manifolds, revealing both conservative and dissipative dynamics, and provides numerous examples illustrating their unique properties.

Contribution

It offers a detailed analysis of conformal Hamiltonian flows, highlighting their mixed conservative and dissipative nature, and constructs diverse examples demonstrating their dynamics.

Findings

Flows exhibit both conservative and dissipative behaviors

Examples show similarities and differences with contact and symplectic cases

Provides a framework for understanding conformal Hamiltonian dynamics

Abstract

We study in detail the dynamics of conformal Hamiltonian flows that are defined on a conformal symplectic manifold (this notion was popularized by Vaisman in 1976). We show that they exhibit some conservative and dissipative behaviours. We also build many examples of various dynamics that show simultaneously their difference and resemblance with the contact and symplectic case.