Self-adjoint Laplacians, symmetric semigroups and diffusions on hyperbolic attractors

Abstract: Analysis on smooth manifolds, foliated spaces and fractals in terms of Dirichlet forms is well established. But such an analysis on hyperbolic attractors is yet to be explored. We use the core material and central results from the theory of hyperbolic dynamical systems such as the stable manifold theorem and physical measures to introduce self-adjoint Laplacians, symmetric Markov semigroups and symmetric diffusions via Dirichlet forms. In particular, this may be seen as far-reaching extension of well-known classical analysis on geodesic flows on manifolds of negative sectional curvature. This talk is based on a joint work with Michael Hinz.

dynamical systems

Audience: researchers in the topic

Bremen Online Dynamics Seminar

Series comments: Talks are approx. 55 min plus discussion. Talks are not recorded.

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