Asymptotic Counting in Conformal Dynamical 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 Asymptotic Counting in Conformal Dynamical Systems write by Mark Pollicott. This book was released on 2021-09-24. Asymptotic Counting in Conformal Dynamical Systems available in PDF, EPUB and Kindle. View the abstract.
Asymptotic Counting in Conformal Dynamical Systems
Asymptotic Counting in Conformal Dynamical 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 Asymptotic Counting in Conformal Dynamical Systems write by Mark Pollicott. This book was released on 2021. Asymptotic Counting in Conformal Dynamical Systems available in PDF, EPUB and Kindle.
Dynamics: Topology and Numbers
Dynamics: Topology and Numbers - 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 Dynamics: Topology and Numbers write by Pieter Moree. This book was released on 2020-02-12. Dynamics: Topology and Numbers available in PDF, EPUB and Kindle. This volume contains the proceedings of the conference Dynamics: Topology and Numbers, held from July 2–6, 2018, at the Max Planck Institute for Mathematics, Bonn, Germany. The papers cover diverse fields of mathematics with a unifying theme of relation to dynamical systems. These include arithmetic geometry, flat geometry, complex dynamics, graph theory, relations to number theory, and topological dynamics. The volume is dedicated to the memory of Sergiy Kolyada and also contains some personal accounts of his life and mathematics.
Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics: Fractals in pure mathematics
Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics: Fractals in pure mathematics - 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 Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics: Fractals in pure mathematics write by David Carfi. This book was released on 2013-10-22. Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics: Fractals in pure mathematics available in PDF, EPUB and Kindle. This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoit Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry (and some aspects of dynamical systems) in pure mathematics. Also included are articles discussing a variety of connections of fractal geometry with other fields of mathematics, including probability theory, number theory, geometric measure theory, partial differential equations, global analysis on non-smooth spaces, harmonic analysis and spectral geometry. The companion volume (Contemporary Mathematics, Volume 601) focuses on applications of fractal geometry and dynamical systems to other sciences, including physics, engineering, computer science, economics, and finance.
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 2011-10-25. 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.
