000 03664nam a22004935i 4500
001 978-3-642-23650-1
003 DE-He213
005 20160624101837.0
007 cr nn 008mamaa
008 111024s2011 gw | s |||| 0|eng d
020 _a9783642236501
_9978-3-642-23650-1
024 7 _a10.1007/978-3-642-23650-1
_2doi
050 4 _aQA313
072 7 _aPBWR
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515.39
_223
082 0 4 _a515.48
_223
100 1 _aMayer, Volker.
_eauthor.
245 1 0 _aDistance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry
_h[electronic resource] /
_cby Volker Mayer, Mariusz Urbanski, Bartlomiej Skorulski.
260 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2011.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2011.
300 _aX, 112p. 3 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2036
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.
520 _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.
650 0 _aMathematics.
650 0 _aDifferentiable dynamical systems.
650 1 4 _aMathematics.
650 2 4 _aDynamical Systems and Ergodic Theory.
700 1 _aUrbanski, Mariusz.
_eauthor.
700 1 _aSkorulski, Bartlomiej.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642236495
786 _dSpringer
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2036
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-23650-1
942 _2EBK1981
_cEBK
999 _c31275
_d31275