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Margulis–Ruelle inequality for general manifolds

Part of: Smooth dynamical systems: general theory Dynamical systems with hyperbolic behavior Ergodic 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: [email protected])
NA QIU
Affiliation:
School of Mathematical Sciences, Center for Dynamical Systems and Differential Equations, Soochow University, Suzhou215006, China (e-mail: [email protected])
*
e-mail: [email protected]
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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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References

Froyland, G., Lloyd, S. and Quas, A.. Coherent structures and isolated spectrum for Perron–Frobenius cocycles. Ergod. Th. & Dynam. Sys. 30 (2010), 729–756.CrossRefGoogle Scholar
Katok, A., Strelcyn, J., Ledrappier, F. and Przytycki, F.. Invariant Manifolds, Entropy and Billiards; Smooth Maps with Singularities (Lecture Notes in Mathematics, 1222). Springer, Berlin, 1986.CrossRefGoogle Scholar
Mañé, R.. Ergodic Theory and Differentiable Dynamics. Springer, Berlin, 1987.CrossRefGoogle Scholar
Oseledets, V. I.. A multiplicative ergodic theorem. Trans. Moscow Math. Soc. 19 (1968), 197–231.Google Scholar
Riquelme, F.. Counterexamples to Ruelle’s inequality in the noncompact case. Ann. Inst. Fourier (Grenoble) 67 (2017), 23–41.CrossRefGoogle Scholar
Ruelle, D.. An inequality for the entropy of differentiable maps. Bol. Soc. Bras. Mat. 9 (1978), 83–88.CrossRefGoogle Scholar