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Author : Dzmitry Badziahin
Publisher : Cambridge University Press
Page : 341 pages
File Size : 29,1 MB
Release : 2016-11-10
Category : Mathematics
ISBN : 1107552370
Presents current research in various topics, including homogeneous dynamics, Diophantine approximation and combinatorics.
Author : Pieter Moree
Publisher : American Mathematical Soc.
Page : 347 pages
File Size : 22,66 MB
Release : 2020-02-12
Category : Education
ISBN : 147045100X
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.
Author : Robert L. Benedetto
Publisher : American Mathematical Soc.
Page : 463 pages
File Size : 15,78 MB
Release : 2019-03-05
Category : Analytic spaces
ISBN : 147044688X
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 : S. F. Koli︠a︡da
Publisher :
Page : 315 pages
File Size : 10,85 MB
Release : 2016
Category : Ergodic theory
ISBN : 9781470434984
This volume contains a collection of survey and research articles from the special program and international conference on Dynamics and Numbers held at the Max-Planck Institute for Mathematics in Bonn, Germany in 2014. The papers reflect the great diversity and depth of the interaction between number theory and dynamical systems and geometry in particular. Topics covered in this volume include symbolic dynamics, Bratelli diagrams, geometry of laminations, entropy, Nielsen theory, recurrence, topology of the moduli space of interval maps, and specification properties
Author : Edson de Faria
Publisher : Cambridge University Press
Page : 192 pages
File Size : 19,80 MB
Release : 2008-10-02
Category : Mathematics
ISBN : 1139474847
Originating with the pioneering works of P. Fatou and G. Julia, the subject of complex dynamics has seen great advances in recent years. Complex dynamical systems often exhibit rich, chaotic behavior, which yields attractive computer generated pictures, for example the Mandelbrot and Julia sets, which have done much to renew interest in the subject. This self-contained book discusses the major mathematical tools necessary for the study of complex dynamics at an advanced level. Complete proofs of some of the major tools are presented; some, such as the Bers-Royden theorem on holomorphic motions, appear for the very first time in book format. An appendix considers Riemann surfaces and Teichmüller theory. Detailing the very latest research, the book will appeal to graduate students and researchers working in dynamical systems and related fields. Carefully chosen exercises aid understanding and provide a glimpse of further developments in real and complex one-dimensional dynamics.
Author : Sergiǐ Kolyada:
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 42,64 MB
Release : 2016-07-27
Category : Mathematics
ISBN : 1470420201
This volume contains a collection of survey and research articles from the special program and international conference on Dynamics and Numbers held at the Max-Planck Institute for Mathematics in Bonn, Germany in 2014. The papers reflect the great diversity and depth of the interaction between number theory and dynamical systems and geometry in particular. Topics covered in this volume include symbolic dynamics, Bratelli diagrams, geometry of laminations, entropy, Nielsen theory, recurrence, topology of the moduli space of interval maps, and specification properties.
Author : A. P. Roberts
Publisher : Cambridge University Press
Page : 390 pages
File Size : 10,22 MB
Release : 2003-05-22
Category : Science
ISBN : 9780521520874
This book uniquely covers both Statics and Dynamics together with a section on background mathematics, providing the student with everything needed to complete typical first year undergraduate courses. Students often find it difficult to visualize problems and grasp the mathematics, but Roberts' friendly approach makes life easier for both student and tutor, tackling concepts from first principles with many examples, exercises and helpful diagrams. The revision section on introductory mathematics is a huge bonus, allowing students to catch up on the pre-requisite mathematics needed to work through both courses.
Author : Vladimir Anashin
Publisher : Walter de Gruyter
Page : 558 pages
File Size : 43,14 MB
Release : 2009-06-02
Category : Mathematics
ISBN : 3110203014
This monograph presents recent developments of the theory of algebraic dynamical systems and their applications to computer sciences, cryptography, cognitive sciences, psychology, image analysis, and numerical simulations. The most important mathematical results presented in this book are in the fields of ergodicity, p-adic numbers, and noncommutative groups. For students and researchers working on the theory of dynamical systems, algebra, number theory, measure theory, computer sciences, cryptography, and image analysis.
Author : Vladimir Anashin
Publisher : Walter de Gruyter
Page : 558 pages
File Size : 42,46 MB
Release : 2009
Category : Mathematics
ISBN : 3110203006
The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Cear , Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
Author : M. Bachir Bekka
Publisher : Cambridge University Press
Page : 214 pages
File Size : 49,84 MB
Release : 2000-05-11
Category : Mathematics
ISBN : 9780521660303
This book, first published in 2000, focuses on developments in the study of geodesic flows on homogenous spaces.