Abstract
We consider a topological dynamical system T:Y→Y on a metric space Y which forms a fibre bundle over another dynamical system. If T is fibrewise expanding and exact along fibres and if ϕ is a Hölder continuous function we prove the existence of a system of conditional measures (called a family of Gibbs measures) where the Jacobian is determined by ϕ. This theorem reduces to Ruelle's Perron–Frobenius theorem when the base of the fibred system consists of a single point. The method of proof does not use any form of symbolic representation. We also study continuity properties of a family of Gibbs measures (over the base) and give applications to the equilibrium theory of higher dimensional complex dynamics.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
