ENTROPY FORMULA FOR SYSTEMS WITH INDUCING SCHEMES

• Type: Article in International Scientific Journal
• Date: 2022

Authors

alves, jf (Author) FCUP; Mesquita, D (Author) Other

Journal

Title: Transactions of the American Mathematical Society

Vol. 376

Pages: 1263-1298

ISSN: 0002-9947

Publisher: American Mathematical Society

Indexing

ISI Web of Knowledge - 0 Citations

Scopus

Other information

Authenticus ID: P-00X-KSZ

DOI: 10.1090/tran/8808

Abstract (EN): We obtain entropy formulas for Sinai-Ruelle-Bowen (SRB) measures with finite entropy given by inducing schemes. In the first part of the work, we obtain Pesin entropy formula for the class of noninvertible systems whose SRB measures are given by Gibbs-Markov induced maps. In the second part, we obtain Pesin entropy formula for invertible maps whose SRB measures are given by Young sets, taking into account a classical compression technique along the stable direction that allows a reduction of the return map associated with a Young set to a Gibbs-Markov map. In both cases, we give applications of our main results to several classes of dynamical systems with singular sets, where the classical results by Ruelle and Pesin cannot be applied. We also present examples of systems with SRB measures given by inducing schemes for which Ruelle inequality does not hold.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 36