The dynamics of conformal Hamiltonian flows: dissipativity and conservativity

Simon Allais ^[1] ; Marie-Claude Arnaud ^[2]
1. [1] University of Strasbourg
  
  University of Strasbourg
  
  Arrondissement de Strasbourg-Ville, Francia
2. [2] Université Paris Cité and Sorbonne Université, France
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 3, 2024, págs. 987-1021
Idioma: inglés
DOI: 10.4171/RMI/1456
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Resumen
- 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.