On topological symplectic dynamical systems

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 determi...

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Autores principales:	Tchuiaga,S., Koivogui,M., Balibuno,F., Mbazumutima,V.
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2017
Materias:	Isotopies Diffeomorphisms Homeomorphisms Displacement energy Hofer-like norms Mass flow Riemannian metric Lefschetz type manifolds Flux geometry.
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462017000200049
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spelling	oai:scielo:S0719-064620170002000492018-04-25On topological symplectic dynamical systemsTchuiaga,S.Koivogui,M.Balibuno,F.Mbazumutima,V. Isotopies Diffeomorphisms Homeomorphisms Displacement energy Hofer-like norms Mass flow Riemannian metric Lefschetz type manifolds Flux geometry. 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.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.19 n.2 20172017-06-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462017000200049en10.4067/S0719-06462017000200049
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Isotopies Diffeomorphisms Homeomorphisms Displacement energy Hofer-like norms Mass flow Riemannian metric Lefschetz type manifolds Flux geometry.
spellingShingle	Isotopies Diffeomorphisms Homeomorphisms Displacement energy Hofer-like norms Mass flow Riemannian metric Lefschetz type manifolds Flux geometry. Tchuiaga,S. Koivogui,M. Balibuno,F. Mbazumutima,V. On topological symplectic dynamical systems
description	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.
author	Tchuiaga,S. Koivogui,M. Balibuno,F. Mbazumutima,V.
author_facet	Tchuiaga,S. Koivogui,M. Balibuno,F. Mbazumutima,V.
author_sort	Tchuiaga,S.
title	On topological symplectic dynamical systems
title_short	On topological symplectic dynamical systems
title_full	On topological symplectic dynamical systems
title_fullStr	On topological symplectic dynamical systems
title_full_unstemmed	On topological symplectic dynamical systems
title_sort	on topological symplectic dynamical systems
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2017
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462017000200049
work_keys_str_mv	AT tchuiagas ontopologicalsymplecticdynamicalsystems AT koivoguim ontopologicalsymplecticdynamicalsystems AT balibunof ontopologicalsymplecticdynamicalsystems AT mbazumutimav ontopologicalsymplecticdynamicalsystems
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On topological symplectic dynamical systems

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