| 000 | 03523nam a22005055i 4500 | ||
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| 001 | 978-3-642-01954-8 | ||
| 003 | DE-He213 | ||
| 005 | 20190213151430.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 100715s2009 gw | s |||| 0|eng d | ||
| 020 |
_a9783642019548 _9978-3-642-01954-8 |
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| 024 | 7 |
_a10.1007/978-3-642-01954-8 _2doi |
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| 072 | 7 |
_aPBWR _2bicssc |
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_aMAT034000 _2bisacsh |
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_aPBWR _2thema |
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| 082 | 0 | 4 |
_a515.39 _223 |
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_a515.48 _223 |
| 100 | 1 |
_aQian, Min. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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| 245 | 1 | 0 |
_aSmooth Ergodic Theory for Endomorphisms _h[electronic resource] / _cby Min Qian, Jian-Sheng Xie, Shu Zhu. |
| 264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2009. |
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| 300 |
_aXIII, 277 p. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
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| 490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1978 |
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| 505 | 0 | _aPreliminaries -- 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. | |
| 520 | _aThis 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 accessible than that of Barreira et al. It also inspires the authors to argue to what extent the famous Eckmann-Ruelle conjecture and many other classical results for diffeomorphisms and for flows hold true. After a careful reading of the book, one can systematically learn the Pesin theory for endomorphisms as well as the typical tricks played in the estimation of the number of balls of certain properties, which are extensively used in Chapters IX and X. | ||
| 650 | 0 | _aDifferentiable dynamical systems. | |
| 650 | 0 | _aMechanical engineering. | |
| 650 | 1 | 4 |
_aDynamical Systems and Ergodic Theory. _0http://scigraph.springernature.com/things/product-market-codes/M1204X |
| 650 | 2 | 4 |
_aMechanical Engineering. _0http://scigraph.springernature.com/things/product-market-codes/T17004 |
| 700 | 1 |
_aXie, Jian-Sheng. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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| 700 | 1 |
_aZhu, Shu. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer eBooks | |
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_iPrinted edition: _z9783642019555 |
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_iPrinted edition: _z9783642019531 |
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_aLecture Notes in Mathematics, _x0075-8434 ; _v1978 |
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| 856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-642-01954-8 |
| 912 | _aZDB-2-SMA | ||
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