Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry write by Volker Mayer. This book was released on 2011-10-25. Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry available in PDF, EPUB and Kindle. 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.
Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry
Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry write by Volker Mayer. This book was released on 2011-10-26. Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry available in PDF, EPUB and Kindle. 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.
Thermodynamic Formalism
Thermodynamic Formalism - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Thermodynamic Formalism write by Mark Pollicott. This book was released on 2021-10-01. Thermodynamic Formalism available in PDF, EPUB and Kindle. This volume arose from a semester at CIRM-Luminy on “Thermodynamic Formalism: Applications to Probability, Geometry and Fractals” which brought together leading experts in the area to discuss topical problems and recent progress. It includes a number of surveys intended to make the field more accessible to younger mathematicians and scientists wishing to learn more about the area. Thermodynamic formalism has been a powerful tool in ergodic theory and dynamical system and its applications to other topics, particularly Riemannian geometry (especially in negative curvature), statistical properties of dynamical systems and fractal geometry. This work will be of value both to graduate students and more senior researchers interested in either learning about the main ideas and themes in thermodynamic formalism, and research themes which are at forefront of research in this area.
Analytic Endomorphisms of the Riemann Sphere
Analytic Endomorphisms of the Riemann Sphere - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Analytic Endomorphisms of the Riemann Sphere write by Mariusz Urbański. This book was released on 2023-09-04. Analytic Endomorphisms of the Riemann Sphere available in PDF, EPUB and Kindle.
Graph Directed Markov Systems
Graph Directed Markov Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Graph Directed Markov Systems write by R. Daniel Mauldin. This book was released on 2003-08-07. Graph Directed Markov Systems available in PDF, EPUB and Kindle. The main focus of this book is the exploration of the geometric and dynamic properties of a far reaching generalization of a conformal iterated function system - a Graph Directed Markov System. These systems are very robust in that they apply to many settings that do not fit into the scheme of conformal iterated systems. The basic theory is laid out here and the authors have touched on many natural questions arising in its context. However, they also emphasise the many issues and current research topics which can be found in original papers. For example the detailed analysis of the structure of harmonic measures of limit sets, the examination of the doubling property of conformal measures, the extensive study of generalized polynomial like mapping or multifractal analysis of geometrically finite Kleinian groups. This book leads readers onto frontier research in the field, making it ideal for both established researchers and graduate students.
