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Record Nr. |
UNISA996466770403316 |
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Autore |
Qian Min <1927-> |
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Titolo |
Smooth ergodic theory for endomorphisms / / Min Qian, Jian-Sheng Xie, Shu Zhu |
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Pubbl/distr/stampa |
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Berlin, Germany : , : Springer, , [2009] |
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©2009 |
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ISBN |
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1-282-65580-9 |
9786612655807 |
3-642-01954-4 |
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Edizione |
[1st ed. 2009.] |
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Descrizione fisica |
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1 online resource (291 p.) |
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Collana |
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Lecture notes in mathematics ; ; 1978 |
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Classificazione |
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Disciplina |
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Soggetti |
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Endomorphisms (Group theory) |
Ergodic theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references (pages [271]-274) and index. |
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Nota di contenuto |
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Preliminaries -- Margulis-Ruelle Inequality -- Expanding Maps -- Axiom A Endomorphisms -- Unstable and Stable Manifolds for Endomorphisms -- Pesin#x2019;s Entropy Formula for Endomorphisms -- SRB Measures and Pesin#x2019;s Entropy Formula for Endomorphisms -- Ergodic Property of Lyapunov Exponents -- Generalized Entropy Formula -- Exact Dimensionality of Hyperbolic Measures. |
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Sommario/riassunto |
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This volume presents a general smooth ergodic theory for deterministic dynamical systems generated by non-invertible endomorphisms, mainly concerning the relations between entropy, Lyapunov exponents and dimensions. The authors make extensive use of the combination of the inverse limit space technique and the techniques developed to tackle random dynamical systems. The most interesting results in this book are (1) the equivalence between the SRB property and Pesin’s entropy formula; (2) the generalized Ledrappier-Young entropy formula; (3) exact-dimensionality for weakly hyperbolic diffeomorphisms and for expanding maps. The proof of the exact-dimensionality for weakly hyperbolic diffeomorphisms seems more |
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