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On topological symplectic dynamical systems

Author
Tchuiaga, S.

Koivogui, M.

Balibuno, F.

Mbazumutima, V.

Full text
https://revistas.ufro.cl/ojs/index.php/cubo/article/view/1578
10.4067/S0719-06462017000200049
Abstract
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.
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Artes, Arquitectura y UrbanismoCiencias Agrarias, Forestales y VeterinariasCiencias Exactas y NaturalesCiencias SocialesDerechoEconomía y AdministraciónFilosofía y HumanidadesIngenieríaMedicinaMultidisciplinarias
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Universidad de ChileUniversidad Católica de ChileUniversidad de Santiago de ChileUniversidad de ConcepciónUniversidad Austral de ChileUniversidad Católica de ValparaísoUniversidad del Bio BioUniversidad de ValparaísoUniversidad Católica del Nortemore

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