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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Analysis Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry
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Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry
Volker Mayer, Bartlomiej Skorulski, Mariusz Urbanski (Broschiert, Englisch)
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Beschreibung
The 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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
26.10.2011
Sprache
Englisch
EAN
9783642236495
Herausgeber
Springer Berlin
Serien- oder Bandtitel
Lecture Notes in Mathematics
Sonderedition
Nein
Autor
Volker Mayer, Bartlomiej Skorulski, Mariusz Urbanski
Seitenanzahl
112
Einbandart
Broschiert
Schlagwörter
37-XX, Hausdorff dimension, multifractal spectrum, random dynamical systems, thermodynamical formalism
Thema-Inhalt
GPFC - Kybernetik und Systemtheorie
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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