LEADER 04053nam 22005775 450 001 996466630603316 005 20200701010927.0 010 $a3-642-23650-2 024 7 $a10.1007/978-3-642-23650-1 035 $a(CKB)3400000000024023 035 $a(SSID)ssj0000609549 035 $a(PQKBManifestationID)11411956 035 $a(PQKBTitleCode)TC0000609549 035 $a(PQKBWorkID)10619067 035 $a(PQKB)10155113 035 $a(DE-He213)978-3-642-23650-1 035 $a(MiAaPQ)EBC3067456 035 $a(PPN)156315645 035 $a(EXLCZ)993400000000024023 100 $a20111024d2011 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aDistance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry$b[electronic resource] /$fby Volker Mayer, Bartlomiej Skorulski, Mariusz Urbanski 205 $a1st ed. 2011. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2011. 215 $a1 online resource (X, 112 p. 3 illus. in color.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2036 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-642-23649-9 320 $aIncludes bibliographical references and index. 327 $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. 330 $aThe theory of random dynamical systems originated from stochastic differential equations. It is intended to provide a framework and techniques to describe and analyze the evolution of dynamical systems when the input and output data are known only approximately, according to some probability distribution. The development of this field, in both the theory and applications, has gone in many directions. In this manuscript we introduce measurable expanding random dynamical systems, develop the thermodynamical formalism and establish, in particular, the exponential decay of correlations and analyticity of the expected pressure although the spectral gap property does not hold. This theory is then used to investigate fractal properties of conformal random systems. We prove a Bowen?s formula and develop the multifractal formalism of the Gibbs states. Depending on the behavior of the Birkhoff sums of the pressure function we arrive at a natural classification of the systems into two classes: quasi-deterministic systems, which share many properties of deterministic ones; and essentially random systems, which are rather generic and never bi-Lipschitz equivalent to deterministic systems. We show that in the essentially random case the Hausdorff measure vanishes, which refutes a conjecture by Bogenschutz and Ochs. Lastly, we present applications of our results to various specific conformal random systems and positively answer a question posed by Bruck and Buger concerning the Hausdorff dimension of quadratic random Julia sets. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2036 606 $aDynamics 606 $aErgodic theory 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 615 0$aDynamics. 615 0$aErgodic theory. 615 14$aDynamical Systems and Ergodic Theory. 676 $a515.39 676 $a515.48 700 $aMayer$b Volker$4aut$4http://id.loc.gov/vocabulary/relators/aut$0478963 702 $aSkorulski$b Bartlomiej$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aUrbanski$b Mariusz$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a996466630603316 996 $aDistance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry$92432631 997 $aUNISA