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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DOI: https://doi.org/10.1007/978-3-642-01954-8_1
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01953-1
Online ISBN: 978-3-642-01954-8
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