Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry

• Published in: Lecture notes in mathematics Vol. 2036
• Main Author: Mayer, Volker
• Format: eBook Book
• Language: English
• Published: Berlin, Heidelberg Springer Nature 2011; Springer Berlin / Heidelberg; Springer Berlin Heidelberg; Springer
• Edition: 1
• Series: Lecture Notes in Mathematics
• Subjects: Dynamical Systems and Ergodic Theory; Exact sciences and technology; Functions, Meromorphic; General mathematics; General, history and biography; Global analysis, analysis on manifolds; Mappings (Mathematics); Mathematics; Mathematics and Statistics; Mathematics. Analysis; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Probability and statistics; Probability theory and stochastic processes; Random dynamical systems; Sciences and techniques of general use; Stochastic analysis; Thermodynamics; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Input output; Correlation; Spectral properties; Gibbs state; Fractal system; Probability distribution; Systems theory; Dynamical system; Stochastic system; Exponential decay; Hausdorff dimension; Spectral gap; Correlation analysis; Classification; Development; Deterministic system; Field theory; Behavior; Random set; Julia set
• ISBN: 3642236502; 9783642236501; 9783642236495; 3642236499
• ISSN: 0075-8434; 1617-9692
• DOI: 10.1007/978-3-642-23650-1

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.