{"id":{"repo_id":"bielefeld","oai_identifier":"oai:pub.uni-bielefeld.de:2961374"},"canonical_url":"https://search.dev.ndltd.org/etd/bielefeld/oai:pub.uni-bielefeld.de:2961374","repository":{"repo_id":"bielefeld","name":"Universität Bielefeld","base_url":"https://pub.uni-bielefeld.de/oai"},"display":{"title":"Self-adjoint Laplacians and Symmetric Diffusions on Hyperbolic Attractors","abstract":"In this thesis analysis on the attractors of hyperbolic dynamical systems is established in terms of Dirichlet forms. We construct self-adjoint Laplacians and symmetric Markov semigroups on uniformly, partially and generalized hyperbolic attractors, as well as on attractors with nonuniformly hyperbolic structure, endowed with SRB measures or Gibbs u-measures. If the measure has full support, we also guarantee the existence of an associated symmetric Hunt diffusion process. We observe some features of such diffusions, for instance, a quasi-invariance property of energy densities in the u-conformal case and the existence of nonconstant harmonic functions of zero energy in the ergodic case. 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.","abstract_html":"In this thesis analysis on the attractors of hyperbolic dynamical systems is established in terms of Dirichlet forms. We construct self-adjoint Laplacians and symmetric Markov semigroups on uniformly, partially and generalized hyperbolic attractors, as well as on attractors with nonuniformly hyperbolic structure, endowed with SRB measures or Gibbs u-measures. If the measure has full support, we also guarantee the existence of an associated symmetric Hunt diffusion process. We observe some features of such diffusions, for instance, a quasi-invariance property of energy densities in the u-conformal case and the existence of nonconstant harmonic functions of zero energy in the ergodic case. 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.","abstract_has_math":false,"creators":["Alikhanloo, Shayan"],"institution":"Universität Bielefeld","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-02-07","date_published":"2022-02-07","updated_at":"2026-07-27T18:50:12Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://pub.uni-bielefeld.de/record/2961374","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Alikhanloo, Shayan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Universitätsbibliothek Bielefeld"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Universität Bielefeld"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis analysis on the attractors of hyperbolic dynamical systems is established in terms of Dirichlet forms. We construct self-adjoint Laplacians and symmetric Markov semigroups on uniformly, partially and generalized hyperbolic attractors, as well as on attractors with nonuniformly hyperbolic structure, endowed with SRB measures or Gibbs u-measures. If the measure has full support, we also guarantee the existence of an associated symmetric Hunt diffusion process. We observe some features of such diffusions, for instance, a quasi-invariance property of energy densities in the u-conformal case and the existence of nonconstant harmonic functions of zero energy in the ergodic case. 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."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Self-adjoint Laplacians and Symmetric Diffusions on Hyperbolic Attractors"]}]}],"canonical_facts":{"dc:creator":["Alikhanloo, Shayan"],"dc:description.abstract":["In this thesis analysis on the attractors of hyperbolic dynamical systems is established in terms of Dirichlet forms. We construct self-adjoint Laplacians and symmetric Markov semigroups on uniformly, partially and generalized hyperbolic attractors, as well as on attractors with nonuniformly hyperbolic structure, endowed with SRB measures or Gibbs u-measures. If the measure has full support, we also guarantee the existence of an associated symmetric Hunt diffusion process. We observe some features of such diffusions, for instance, a quasi-invariance property of energy densities in the u-conformal case and the existence of nonconstant harmonic functions of zero energy in the ergodic case. 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."],"dc:format.medium":["application/pdf"],"dc:publisher":["Universitätsbibliothek Bielefeld"],"dc:title":["Self-adjoint Laplacians and Symmetric Diffusions on Hyperbolic Attractors"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Bielefeld"]},"updated_at":"2026-07-27T18:50:12Z"}