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Author : Robert L. Benedetto
Release : 2019
Genre : Analytic spaces
Kind : eBook
Book Rating : 066/5 ( reviews)
Book Synopsis Dynamics in One Non-archimedean Variable by : Robert L. Benedetto
Download or read book Dynamics in One Non-archimedean Variable written by Robert L. Benedetto. This book was released on 2019. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert L. Benedetto
Release : 2019-03-05
Genre : Analytic spaces
Kind : eBook
Book Rating : 88X/5 ( reviews)
Book Synopsis Dynamics in One Non-Archimedean Variable by : Robert L. Benedetto
Download or read book Dynamics in One Non-Archimedean Variable written by Robert L. Benedetto. This book was released on 2019-03-05. Available in PDF, EPUB and Kindle. Book excerpt: The theory of complex dynamics in one variable, initiated by Fatou and Julia in the early twentieth century, concerns the iteration of a rational function acting on the Riemann sphere. Building on foundational investigations of p-adic dynamics in the late twentieth century, dynamics in one non-archimedean variable is the analogous theory over non-archimedean fields rather than over the complex numbers. It is also an essential component of the number-theoretic study of arithmetic dynamics. This textbook presents the fundamentals of non-archimedean dynamics, including a unified exposition of Rivera-Letelier's classification theorem, as well as results on wandering domains, repelling periodic points, and equilibrium measures. The Berkovich projective line, which is the appropriate setting for the associated Fatou and Julia sets, is developed from the ground up, as are relevant results in non-archimedean analysis. The presentation is accessible to graduate students with only first-year courses in algebra and analysis under their belts, although some previous exposure to non-archimedean fields, such as the p-adic numbers, is recommended. The book should also be a useful reference for more advanced students and researchers in arithmetic and non-archimedean dynamics.
Author : Henk Bruin
Release : 2023-01-20
Genre : Mathematics
Kind : eBook
Book Rating : 847/5 ( reviews)
Book Synopsis Topological and Ergodic Theory of Symbolic Dynamics by : Henk Bruin
Download or read book Topological and Ergodic Theory of Symbolic Dynamics written by Henk Bruin. This book was released on 2023-01-20. Available in PDF, EPUB and Kindle. Book excerpt: Symbolic dynamics is essential in the study of dynamical systems of various types and is connected to many other fields such as stochastic processes, ergodic theory, representation of numbers, information and coding, etc. This graduate text introduces symbolic dynamics from a perspective of topological dynamical systems and presents a vast variety of important examples. After introducing symbolic and topological dynamics, the core of the book consists of discussions of various subshifts of positive entropy, of zero entropy, other non-shift minimal action on the Cantor set, and a study of the ergodic properties of these systems. The author presents recent developments such as spacing shifts, square-free shifts, density shifts, $mathcal{B}$-free shifts, Bratteli-Vershik systems, enumeration scales, amorphic complexity, and a modern and complete treatment of kneading theory. Later, he provides an overview of automata and linguistic complexity (Chomsky's hierarchy). The necessary background for the book varies, but for most of it a solid knowledge of real analysis and linear algebra and first courses in probability and measure theory, metric spaces, number theory, topology, and set theory suffice. Most of the exercises have solutions in the back of the book.
Author : Fernando Q. Gouvêa
Release : 2020-06-19
Genre : Mathematics
Kind : eBook
Book Rating : 957/5 ( reviews)
Book Synopsis p-adic Numbers by : Fernando Q. Gouvêa
Download or read book p-adic Numbers written by Fernando Q. Gouvêa. This book was released on 2020-06-19. Available in PDF, EPUB and Kindle. Book excerpt: There are numbers of all kinds: rational, real, complex, p-adic. The p-adic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. This elementary introduction offers a broad understanding of p-adic numbers. From the reviews: "It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is." --THE MATHEMATICAL GAZETTE
Author : Volodymyr Nekrashevych
Release : 2022-10-11
Genre : Mathematics
Kind : eBook
Book Rating : 205/5 ( reviews)
Book Synopsis Groups and Topological Dynamics by : Volodymyr Nekrashevych
Download or read book Groups and Topological Dynamics written by Volodymyr Nekrashevych. This book was released on 2022-10-11. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to group-theoretic aspects of topological dynamics such as studying groups using their actions on topological spaces, using group theory to study symbolic dynamics, and other connections between group theory and dynamical systems. One of the main applications of this approach to group theory is the study of asymptotic properties of groups such as growth and amenability. The book presents recently developed techniques of studying groups of dynamical origin using the structure of their orbits and associated groupoids of germs, applications of the iterated monodromy groups to hyperbolic dynamical systems, topological full groups and their properties, amenable groups, groups of intermediate growth, and other topics. The book is suitable for graduate students and researchers interested in group theory, transformations defined by automata, topological and holomorphic dynamics, and theory of topological groupoids. Each chapter is supplemented by exercises of various levels of complexity.
