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Abstract integration, Combinatorics of Trees and Differential Equations

dc.contributor.authorGubinelli, Massimiliano
dc.date.accessioned2010-02-11T10:49:45Z
dc.date.available2010-02-11T10:49:45Z
dc.date.issued2011
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/3408
dc.language.isoenen
dc.subjectEquations différentielles
dc.subjectMathematical Physics
dc.subject.ddc515en
dc.titleAbstract integration, Combinatorics of Trees and Differential Equations
dc.typeChapitre d'ouvrage
dc.description.abstractenThis is a review paper on recent work about the connections between rough path theory, the Connes-Kreimer Hopf algebra on rooted trees and the analysis of finite and infinite dimensional differential equation. We try to explain and motivate the theory of rough paths introduced by T. Lyons in the context of differential equations in presence of irregular noises. We show how it is used in an abstract algebraic approach to the definition of integrals over paths which involves a cochain complex of finite increments. In the context of such abstract integration theories we outline a connection with the combinatorics of rooted trees. As interesting examples where these ideas apply we present two infinite dimensional dynamical systems: the Navier-Stokes equation and the Korteweg-de-Vries equation.
dc.identifier.citationpages135-152
dc.relation.ispartoftitleCombinatorics and Physics
dc.relation.ispartofeditorKurusch Ebrahimi-Fard, Matilde Marcolli, Walter D. van Suijlekom
dc.relation.ispartofpublnameAmerican Mathematical Society
dc.relation.ispartofpublcityProvidence, R.I.
dc.relation.ispartofdate2011
dc.relation.ispartofurl10.1090/conm/539
dc.identifier.urlsitehttps://arxiv.org/abs/0809.1821v1
dc.description.sponsorshipprivateouien
dc.subject.ddclabelAnalyseen
dc.relation.ispartofisbn978-0-8218-5329-0
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dc.description.halcandidateoui
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dc.description.audienceInternational
dc.date.updated2017-03-13T15:14:27Z


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