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Continuity of the SRB entropy of convex projective structures

Part of: Real and complex geometry

Published online by Cambridge University Press:  04 June 2020

PATRICK FOULON  and
INKANG KIM
PATRICK FOULON
Affiliation:
Aix-Marseille Université, CNRS, Société Mathématique de France, CIRM (Centre International de Rencontres Mathématiques), Marseille, France UMR 822, 163 avenue de Luminy, 13288 Marseille cedex 9, France (e-mail: foulon@cirm-math.fr)
INKANG KIM
Affiliation:
School of Mathematics, KIAS, Heogiro 85, Dongdaemen-gu, Seoul 02455, Korea (e-mail: inkang@kias.re.kr)
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Abstract

The space of convex projective structures has been well studied with respect to the topological entropy. But, to better understand the geometry of the structure, we study the entropy of the Sinai–Ruelle–Bowen measure and show that it is a continuous function on the space of strictly convex real projective structures.

Keywords

real projective structureSinai–Ruelle–Bowen measureentropy

MSC classification

Primary: 51M10: Hyperbolic and elliptic geometries (general) and generalizations
Secondary: 57S25: Groups acting on specific manifolds
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 8 , August 2021 , pp. 2369 - 2381
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Copyright
© The Author(s) 2020. Published by Cambridge University Press

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