Entropy formula and continuity of entropy for piecewise expanding maps

• Type: Article in International Scientific Journal
• Date: 2021

Authors

alves, jf (Author) FCUP; Pumarino, A (Author) Other

Journal

The Journal is awaiting validation by the Administrative Services.

Title: Annales de l'Institut Henri Poincaré, série C: Analyse non linéaire

Vol. 38

Pages: 91-108

ISSN: 0294-1449

Publisher: EMS Press

Indexing

ISI Web of Knowledge - 3 Citations

Scopus - 3 Citations

Other information

Authenticus ID: P-00S-CFP

DOI: 10.1016/j.anihpc.2020.06.003

Abstract (EN): We consider some classes of piecewise expanding maps in finite dimensional spaces having invariant probability measures which are absolutely continuous with respect to Lebesgue measure. We derive an entropy formula for such measures and, using this entropy formula, we present sufficient conditions for the continuity of that entropy with respect to the parameter in some parametrized families of maps. We apply our results to a classical one-dimensional family of tent maps and a family of two-dimensional maps which arises as the limit of return maps when a homoclinic tangency is unfolded by a family of three dimensional diffeomorphisms.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 18