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On bifurcation of statistical properties of partially hyperbolic endomorphisms

Part of: Dynamical systems with hyperbolic behavior Smooth dynamical systems: general theory

Published online by Cambridge University Press:  18 April 2023

MASATO TSUJII Open the ORCID record for MASATO TSUJII [Opens in a new window]  and
ZHIYUAN ZHANG
MASATO TSUJII
Affiliation:
Department of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
ZHIYUAN ZHANG
Affiliation:
CNRS, Institut Galilée, Université Paris 13, 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France
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Abstract

We give an example of a path-wise connected open set of $C^{\infty }$ partially hyperbolic endomorphisms on the $2$-torus, on which the (unique) Sinai–Ruelle–Bowen (SRB) measure exists for each system and varies smoothly depending on the system, while the sign of its central Lyapunov exponent changes.

Keywords

Sinai–Bowen–Ruelle measurepartially hyperbolic endomorphismLyapunov exponent

MSC classification

Primary: 37C30: Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems
Secondary: 37C40: Smooth ergodic theory, invariant measures 37D30: Partially hyperbolic systems and dominated splittings
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 44 , Issue 3 , March 2024 , pp. 933 - 944
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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