Rough Center Manifolds

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NEAMTU, Alexandra, Christian KUEHN, 2021. Rough Center Manifolds. In: SIAM Journal on Mathematical Analysis. SIAM. 53(4), pp. 3912-3957. ISSN 0036-1410. eISSN 1095-7154. Available under: doi: 10.1137/18M1234084

@article{Neamtu2021Rough-57942, title={Rough Center Manifolds}, year={2021}, doi={10.1137/18M1234084}, number={4}, volume={53}, issn={0036-1410}, journal={SIAM Journal on Mathematical Analysis}, pages={3912--3957}, author={Neamtu, Alexandra and Kuehn, Christian} }

<rdf:RDF xmlns:dcterms="" xmlns:dc="" xmlns:rdf="" xmlns:bibo="" xmlns:dspace="" xmlns:foaf="" xmlns:void="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dcterms:title>Rough Center Manifolds</dcterms:title> <dspace:isPartOfCollection rdf:resource=""/> <dcterms:isPartOf rdf:resource=""/> <dc:rights>terms-of-use</dc:rights> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dc:creator>Neamtu, Alexandra</dc:creator> <dc:date rdf:datatype="">2022-07-05T11:23:31Z</dc:date> <bibo:uri rdf:resource=""/> <dc:creator>Kuehn, Christian</dc:creator> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dcterms:rights rdf:resource=""/> <dcterms:abstract xml:lang="eng">Since the breakthrough in rough paths theory for stochastic ordinary differential equations, there has been a strong interest in investigating the rough differential equation (RDE) approach and its numerous applications. Rough path techniques can stay closer to deterministic analytical methods and have the potential to transfer many pathwise ordinary differential equation (ODE) techniques more directly to a stochastic setting. However, there are few works that analyze dynamical properties of RDEs and connect the rough path/regularity structures, ODE, and random dynamical systems approaches. Here we contribute to this aspect and analyze invariant manifolds for RDEs. By means of a suitably discretized Lyapunov--Perron-type method we prove the existence and regularity of local center manifolds for such systems. Our method directly works with the RDE and we exploit rough paths estimates to obtain the relevant contraction properties of the Lyapunov--Perron map.</dcterms:abstract> <dcterms:issued>2021</dcterms:issued> <dc:contributor>Kuehn, Christian</dc:contributor> <dcterms:available rdf:datatype="">2022-07-05T11:23:31Z</dcterms:available> <dc:language>eng</dc:language> <dc:contributor>Neamtu, Alexandra</dc:contributor> </rdf:Description> </rdf:RDF>

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