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024 7 _a10.1007/978-3-642-23650-1
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037 _bSpringer
050 4 _aQA614.835
_b.M39 2011
072 7 _aPBWR
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072 7 _aMAT034000
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082 0 4 _a515/.39
_223
049 _aMAIN
100 1 _aMayer, Volker,
_d1964-
_1https://id.oclc.org/worldcat/entity/E39PBJbGXC8QyJgxMYPtXkCvpP
_978689
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.
300 _a1 online resource (x, 112 pages) :
_billustrations (some color)
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
347 _bPDF
490 1 _aLecture notes in mathematics,
_x0075-8434 ;
_v2036
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
650 0 _aFractals.
_911007
650 6 _aSystèmes dynamiques aléatoires.
_9969805
650 6 _aFractales.
_970338
650 7 _afractals.
_2aat
_911007
650 7 _aFractales
_2embne
_970338
650 7 _aFractals
_2fast
_911007
650 7 _aRandom dynamical systems
_2fast
_969582
653 _aMathematics
653 _aDifferentiable dynamical systems
653 _aDynamical Systems and Ergodic Theory
700 1 _aSkorulski, Bartlomiej.
_978690
700 1 _aUrbański, Mariusz.
_978691
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
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.
856 4 0 _uhttps://link-springer-com.libraryproxy.ist.ac.at/10.1007/978-3-642-23650-1
938 _aAskews and Holts Library Services
_bASKH
_nAH26854954
938 _aProQuest Ebook Central
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938 _aebrary
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938 _aYBP Library Services
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994 _a92
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