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.
@article{1578,
title = {On topological symplectic dynamical systems},
journal = {CUBO, A Mathematical Journal},
volume = {19},
year = {2017},
language = {en},
url = {http://dml.mathdoc.fr/item/1578}
}
Tchuiaga, S.; Koivogui, M.; Balibuno, F.; Mbazumutima, V. On topological symplectic dynamical systems. CUBO, A Mathematical Journal, Tome 19 (2017) . http://gdmltest.u-ga.fr/item/1578/