On topological symplectic dynamical systems
- S. Tchuiaga tchuiagas@gmail.com
- M. Koivogui moussa.koivogui@esatic.ci
- F. Balibuno balibuno.lugando@imsp-uac.org
- V. Mbazumutima mbazumutima.vianney@aims-cameroon.org
Downloads
DOI:
https://doi.org/10.4067/S0719-06462017000200049Abstract
This paper contributes to the study of topological symplectic dynamical systems, and hence to the extension of smooth symplectic dynamical systems. Using the positivity result of symplectic displacement energy [4], we prove that any generator of a strong symplectic isotopy uniquely determine the latter. This yields a symplectic analogue of a result proved by Oh [12], and the converse of the main theorem found in [6]. Also, tools for defining and for studying the topological symplectic dynamical systems are provided: We construct a right-invariant metric on the group of strong symplectic homeomorphisms whose restriction to the group of all Hamiltonian homeomorphism is equivalent to Oh‘s metric [12], define the topological analogues of the usual symplectic displacement energy for non-empty open sets, and we prove that the latter is positive. Several open conjectures are elaborated.