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Margulis–Ruelle inequality for general manifolds

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

Published online by Cambridge University Press:  22 April 2021

GANG LIAO  and
NA QIU
GANG LIAO*
Affiliation:
School of Mathematical Sciences, Center for Dynamical Systems and Differential Equations, Soochow University, Suzhou215006, China (e-mail: na.qiu@qq.com)
NA QIU
Affiliation:
School of Mathematical Sciences, Center for Dynamical Systems and Differential Equations, Soochow University, Suzhou215006, China (e-mail: na.qiu@qq.com)
*
e-mail: lg@suda.edu.cn
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Abstract

In this paper we investigate the Margulis–Ruelle inequality for general Riemannian manifolds (possibly non-compact and with a boundary) and show that it always holds under an integrable condition.

Keywords

boundaryLyapunov exponentmetric entropynon-compactness

MSC classification

Primary: 37A35: Entropy and other invariants, isomorphism, classification
Secondary: 37C40: Smooth ergodic theory, invariant measures 37D50: Hyperbolic systems with singularities (billiards, etc.)
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 6 , June 2022 , pp. 2064 - 2079
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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