Self-adjoint Laplacians on partially and generalized hyperbolic attractors
Dynamical Systems
2021-05-11 v1 Functional Analysis
Probability
Abstract
We construct self-adjoint Laplacians and symmetric Markov semigroups on partially hyperbolic attractors and on hyperbolic attractors with singularities, endowed with Gibbs u-measures. If the measure has full support, we can also guarantee the existence of an associated symmetric Hunt diffusion process. In the special case of partially hyperbolic diffeomorphisms induced by geodesic flows on manifolds of negative sectional curvature the Laplacians we consider are self-adjoint extensions of well-known classical leafwise Laplacians.
Cite
@article{arxiv.2105.04470,
title = {Self-adjoint Laplacians on partially and generalized hyperbolic attractors},
author = {Shayan Alikhanloo and Michael Hinz},
journal= {arXiv preprint arXiv:2105.04470},
year = {2021}
}