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Preliminaries

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1978)

Abstract

In this part we review some necessary concepts and results from ergodic theory, which will be frequently used in this monograph.

Throughout this book, M is an m 0-dimensional, smooth, compact and connected Riemannian manifold without boundary.We use f ∈ C r(O,M) to denote a C r map from O to M, where O is an open subset of M, and we call f a C r endomorphism on M if f ∈ C r (M, M). We use T f to denote the tangent map induced by f when r ≥ 1.

For any compact metrizable space X and continuous map T : X → X, We use M T (X) to denote the set of T-invariant Borel probability measures on X.

Keywords

  • Lyapunov Exponent
  • Borel Probability Measure
  • Connected Riemannian Manifold
  • Compact Metrizable Space
  • Multiplicative Ergodic Theorem

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2009 Springer-Verlag Berlin Heidelberg

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QUIAN, M., XIE, JS., ZHU, S. (2009). Preliminaries. 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_1

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