Topological Dynamics via Structured Koopman Subsystems

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dc.contributor.advisor Nagel, Rainer (Prof. Dr.)
dc.contributor.author Küster, Kari Valentina
dc.date.accessioned 2021-12-15T08:07:55Z
dc.date.available 2021-12-15T08:07:55Z
dc.date.issued 2021-12-15
dc.identifier.uri http://hdl.handle.net/10900/121768
dc.identifier.uri http://nbn-resolving.de/urn:nbn:de:bsz:21-dspace-1217682 de_DE
dc.identifier.uri http://dx.doi.org/10.15496/publikation-63134
dc.description.abstract This thesis deals with the interplay of quotient systems of a topological dynamical system and subsystems of its corresponding Koopman system. It begins with a historical „prelude“ (in German) where biographical aspects of the involved mathematicians are highlighted. In Chapter 1 topological dynamical systems and their corresponding Koopman systems are introduced and the correspondence of quotient systems and subsystems is explained. Chapter 2 is devoted to the simplest subsystem of a Koopman system, the fixed space. A dynamical description of the corresponding quotient system of the dynamical system is derived via a hierarchy of transfinite orbits. In particular, this leads to the characterization of a one-dimensional fixed space. In Chapter 3 the Lyapunov algebra is defined which is generated by so-called Lyapunov functions. Its properties, special cases and its connection to the generalized recurrent set are discussed. Also algebras which are generated by a single Lyapunov function are considered and extended Lyapunov functions are introduced. Finally, decompositions of the state space obtained by the Lyapunov algebra are studied. en
dc.language.iso de de_DE
dc.language.iso en de_DE
dc.publisher Universität Tübingen de_DE
dc.rights ubt-podok de_DE
dc.rights.uri http://tobias-lib.uni-tuebingen.de/doku/lic_mit_pod.php?la=de de_DE
dc.rights.uri http://tobias-lib.uni-tuebingen.de/doku/lic_mit_pod.php?la=en en
dc.subject.classification Topologische Dynamik , Funktionalanalysis , Subsystem , Ljapunov-Funktion , Ergodentheorie de_DE
dc.subject.ddc 510 de_DE
dc.subject.other ergodic theory en
dc.subject.other verallgemeinerte rekurrente Menge de_DE
dc.subject.other topological dynamics en
dc.subject.other functional analysis en
dc.subject.other Lyapunovalgebra de_DE
dc.subject.other Fixraum de_DE
dc.subject.other subsystem en
dc.subject.other Zerlegung de_DE
dc.subject.other Lyapunov function en
dc.subject.other Koopman operator en
dc.subject.other topologische Ergodizität de_DE
dc.subject.other generalized recurrent set en
dc.subject.other Quotientensystem de_DE
dc.subject.other Koopmanoperator de_DE
dc.subject.other Lyapunov algebra en
dc.subject.other fixed space en
dc.subject.other decomposition en
dc.subject.other topological ergodicity en
dc.subject.other quotient system en
dc.subject.other Conley decomposition en
dc.title Topological Dynamics via Structured Koopman Subsystems en
dc.type Dissertation de_DE
dcterms.dateAccepted 2021-09-24
utue.publikation.fachbereich Mathematik de_DE
utue.publikation.fakultaet 7 Mathematisch-Naturwissenschaftliche Fakultät de_DE
utue.publikation.noppn yes de_DE

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