| 000 | 05920cam a2200841 a 4500 | ||
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| 001 | ocn759858108 | ||
| 003 | OCoLC | ||
| 005 | 20250703133256.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 111107s2011 gw a ob 001 0 eng d | ||
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_a10.1007/978-3-642-23650-1 _2doi |
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| 037 | _bSpringer | ||
| 050 | 4 |
_aQA614.835 _b.M39 2011 |
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_aMAT034000 _2bisacsh |
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_a515/.39 _223 |
| 049 | _aMAIN | ||
| 100 | 1 |
_aMayer, Volker, _d1964- _1https://id.oclc.org/worldcat/entity/E39PBJbGXC8QyJgxMYPtXkCvpP _978689 |
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| 245 | 1 | 0 |
_aDistance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry / _cVolker Mayer, Bartlomiej Skorulski, Mariusz Urbanski. |
| 260 |
_aHeidelberg ; _aNew York : _bSpringer-Verlag Berlin Heidelberg, _c©2011. |
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| 300 |
_a1 online resource (x, 112 pages) : _billustrations (some color) |
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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 | ||
| 347 | _bPDF | ||
| 490 | 1 |
_aLecture notes in mathematics, _x0075-8434 ; _v2036 |
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| 504 | _aIncludes bibliographical references (pages 109-110) and index. | ||
| 520 | 8 | _aAnnotation The theory of random dynamical systems originated from stochasticdifferential equations. It is intended to provide a framework andtechniques to describe and analyze the evolution of dynamicalsystems when the input and output data are known only approximately, according to some probability distribution. The development of this field, in both the theory and applications, has gone in many directions. In this manuscript we introduce measurable expanding random dynamical systems, develop the thermodynamical formalism and establish, in particular, the exponential decay of correlations and analyticity of the expected pressure although the spectral gap property does not hold. This theory is then used to investigate fractal properties of conformal random systems. We prove a Bowens formula and develop the multifractal formalism of the Gibbs states. Depending on the behavior of the Birkhoff sums of the pressure function we arrive at a natural classification of the systems into two classes: quasi-deterministic systems, which share manyproperties of deterministic ones; and essentially random systems, which are rather generic and never bi-Lipschitz equivalent to deterministic systems. We show that in the essentially random case the Hausdorff measure vanishes, which refutes a conjecture by Bogenschutz and Ochs. Lastly, we present applications of our results to various specific conformal random systems and positively answer a question posed by Bruck and Buger concerning the Hausdorff dimension of quadratic random Julia sets. | |
| 505 | 0 | _a1 Introduction -- 2 Expanding Random Maps -- 3 The RPF-theorem -- 4 Measurability, Pressure and Gibbs Condition -- 5 Fractal Structure of Conformal Expanding Random Repellers -- 6 Multifractal Analysis -- 7 Expanding in the Mean -- 8 Classical Expanding Random Systems -- 9 Real Analyticity of Pressure. | |
| 546 | _aEnglish. | ||
| 650 | 0 |
_aRandom dynamical systems. _969582 |
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| 650 | 0 |
_aFractals. _911007 |
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| 650 | 6 |
_aSystèmes dynamiques aléatoires. _9969805 |
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| 650 | 6 |
_aFractales. _970338 |
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| 650 | 7 |
_afractals. _2aat _911007 |
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| 650 | 7 |
_aFractales _2embne _970338 |
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| 650 | 7 |
_aFractals _2fast _911007 |
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| 650 | 7 |
_aRandom dynamical systems _2fast _969582 |
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| 653 | _aMathematics | ||
| 653 | _aDifferentiable dynamical systems | ||
| 653 | _aDynamical Systems and Ergodic Theory | ||
| 700 | 1 |
_aSkorulski, Bartlomiej. _978690 |
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| 700 | 1 |
_aUrbański, Mariusz. _978691 |
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| 758 |
_ihas work: _aDistance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry (Text) _1https://id.oclc.org/worldcat/entity/E39PCGmcfWy39TBJFyjjk7BbQy _4https://id.oclc.org/worldcat/ontology/hasWork |
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| 773 | 0 | _tSpringer eBooks | |
| 776 | 0 | 8 |
_iPrint version: _aMayer, Volker, 1964- _tDistance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry. _dHeidelberg ; New York : Springer-Verlag Berlin Heidelberg, ©2011 _w(DLC) 2011940286 |
| 830 | 0 |
_aLecture notes in mathematics (Springer-Verlag) ; _v2036. |
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| 856 | 4 | 0 | _uhttps://link-springer-com.libraryproxy.ist.ac.at/10.1007/978-3-642-23650-1 |
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