dc.contributor.author
Schneider, Isabelle Anne Nicole
dc.date.accessioned
2023-10-31T09:05:07Z
dc.date.available
2023-10-31T09:05:07Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/41223
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-40944
dc.description.abstract
Going back to Henri Poincaré, the main concern of the theory of dynamical systems for differential equations is the qualitative characterization of solutions. Symmetries, described by group transformations, help immensely in this quest --- providing that they exist, which is often the case only in very special dynamical systems. In this thesis, we significantly enlarge the class of dynamical systems which can be studied by symmetry methods, moving our focus from groups to groupoids as the underlying algebraic structure describing symmetry. Building on the groupoid framework, we fundamentally generalize the notion of equivariance and equivariant bifurcation theory. In summary, we present a new unified theory of symmetric spatio-temporal patterns.
en
dc.format.extent
166 Seiten
dc.rights.uri
http://www.fu-berlin.de/sites/refubium/rechtliches/Nutzungsbedingungen
dc.subject
bifurcation theory
en
dc.subject
differential equations
en
dc.subject
dynamical systems
en
dc.subject
equivariance
en
dc.subject.ddc
500 Naturwissenschaften und Mathematik::510 Mathematik::515 Analysis
dc.title
Symmetry Groupoids in Dynamical Systems
dc.contributor.gender
female
dc.contributor.firstReferee
Stevens, Angela
dc.contributor.furtherReferee
Verdun Lunel, Sjoerd
dc.date.accepted
2023-05-25
dc.identifier.urn
urn:nbn:de:kobv:188-refubium-41223-1
dc.title.subtitle
Spatio-temporal Patterns and a Generalized Equivariant Bifurcation Theory
dc.title.translated
Symmetrie-Gruppoide in dynamischen Systemen
ger
refubium.affiliation
Mathematik und Informatik
dcterms.accessRights.dnb
free
dcterms.accessRights.openaire
open access
dcterms.accessRights.proquest
accept