Abstract
Margulis-Ruelle inequality is a basic and important fact in the ergodic theory of smooth dynamical systems, which relates the two key concepts: metric entropy and Lyapunov exponents. It asserts that the entropy can be bounded above by the sum of the positive Lyapunov exponents. Margulis first proved the result for diffeomorphisms preserving a smooth measure. The general statement due to Ruelle [77]. Rigorous proofs are available in several books for the case of diffeomorphisms, see [32] and [57]. A generalization of the result to random diffeomorphisms is given by [51]. In this chapter we present a rigorous proof for the general case, which is valid for non-invertible C 1 maps.
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© 2009 Springer-Verlag Berlin Heidelberg
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QUIAN, M., XIE, JS., ZHU, S. (2009). Margulis-Ruelle Inequality. In: Smooth Ergodic Theory for Endomorphisms. Lecture Notes in Mathematics(), vol 1978. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01954-8_2
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DOI: https://doi.org/10.1007/978-3-642-01954-8_2
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Publisher Name: Springer, Berlin, Heidelberg
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Online ISBN: 978-3-642-01954-8
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