Abstract integration, Combinatorics of Trees and Differential Equations
Gubinelli, Massimiliano (2011), Abstract integration, Combinatorics of Trees and Differential Equations, in Kurusch Ebrahimi-Fard, Matilde Marcolli, Walter D. van Suijlekom, Combinatorics and Physics, American Mathematical Society : Providence, R.I., p. 135-152
External document linkhttps://arxiv.org/abs/0809.1821v1
Book titleCombinatorics and Physics
Book authorKurusch Ebrahimi-Fard, Matilde Marcolli, Walter D. van Suijlekom
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Abstract (EN)This 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.
Subjects / KeywordsEquations différentielles; Mathematical Physics
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