Algebraic Structure Of Dynamical Systems
DOWNLOAD
Download Algebraic Structure Of Dynamical Systems PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Algebraic Structure Of Dynamical Systems book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Algebraic Structure Of Dynamical Systems
DOWNLOAD
Author : James P. Talisse
language : en
Publisher:
Release Date : 2017
Algebraic Structure Of Dynamical Systems written by James P. Talisse and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Dynamics categories.
A dynamical system is a mathematical object which describes the motion of a set of points over time. Dynamical systems can be used to study differential equations, cryptography, computer science, and even biology. Viewed as a purely mathematical object, one can ask questions about the behavior of the dynamical system based on the structure of algebraic objects associated with it. In this project we study two algebraic objects, centralizers and topological full groups, associated to symbolic dynamical systems. The centralizer group tells us about the symmetries a system possesses. Results relating to the centralizer historically have indicated that the more complex the dynamical system is, captured by the Topological Entropy, the more structure its centralizer has. Similarly, low complexity systems have been shown to have very simple centralizers. This seems to suggest that one can recover information about the dynamical system based upon its centralizer group. In particular, if a system is known to have a certain centralizer group, we might want to draw conclusions about the complexity of the system. In this project we present a class of high complexity systems which have a very rigid centralizer, which shows the relationship is more subtle than may have been originally thought. We also study the topological full group of a dynamical system. This group completely defines the system up to time reversal. We apply numerical estimates to draw conclusions about the algebraic properties of this group. In particular, we seek to know when the topological full group of a dynamical system is amenable. Amenability is an algebraic property that can be thought of as having a probability measure on G. This measure would answer the question: given a subset A of G, what is the probability that a random element of G is in A? We apply Grigorchuk’s amenability criterion to answer this question. Both these results provide us with information about the algebraic structure of dynamical systems. If we know certain information about the different groups associated with a dynamical system, we can make conclusions about the system itself. As such, questions about dynamical systems can now become questions about algebra, and vice versa. These results mostly reveal the structure of symbolic dynamical systems and address the fundamental question of mathematics about what is possible. However, our construction of a positive entropy system with trivial centralizer can be interpreted as the existence of an information channel with positive capacity that cannot be encrypted with substitution ciphers.
On The Algebraic Structure Of Dynamical Systems
DOWNLOAD
Author : Daniel Halpern-Leistner
language : en
Publisher:
Release Date : 2007
On The Algebraic Structure Of Dynamical Systems written by Daniel Halpern-Leistner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
Applied Algebraic Dynamics
DOWNLOAD
Author : Vladimir Anashin
language : en
Publisher: Walter de Gruyter
Release Date : 2009
Applied Algebraic Dynamics written by Vladimir Anashin and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
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)
Partial Dynamical Systems Fell Bundles And Applications
DOWNLOAD
Author : Ruy Exel
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-09-20
Partial Dynamical Systems Fell Bundles And Applications written by Ruy Exel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-20 with Banach spaces categories.
Partial dynamical systems, originally developed as a tool to study algebras of operators in Hilbert spaces, has recently become an important branch of algebra. Its most powerful results allow for understanding structural properties of algebras, both in the purely algebraic and in the C*-contexts, in terms of the dynamical properties of certain systems which are often hiding behind algebraic structures. The first indication that the study of an algebra using partial dynamical systems may be helpful is the presence of a grading. While the usual theory of graded algebras often requires gradings to be saturated, the theory of partial dynamical systems is especially well suited to treat nonsaturated graded algebras which are in fact the source of the notion of “partiality”. One of the main results of the book states that every graded algebra satisfying suitable conditions may be reconstructed from a partial dynamical system via a process called the partial crossed product. Running in parallel with partial dynamical systems, partial representations of groups are also presented and studied in depth. In addition to presenting main theoretical results, several specific examples are analyzed, including Wiener–Hopf algebras and graph C*-algebras.
Symmetries And Singularity Structures
DOWNLOAD
Author : Muthuswamy Lakshmanan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Symmetries And Singularity Structures written by Muthuswamy Lakshmanan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Proceedings of the Workshop, Bharathidasan University, Tiruchirapalli, India, November 29 - December 2, 1989
Structure Of Dynamical Systems
DOWNLOAD
Author : J.M. Souriau
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Structure Of Dynamical Systems written by J.M. Souriau and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The aim of the book is to treat all three basic theories of physics, namely, classical mechanics, statistical mechanics, and quantum mechanics from the same perspective, that of symplectic geometry, thus showing the unifying power of the symplectic geometric approach. Reading this book will give the reader a deep understanding of the interrelationships between the three basic theories of physics. This book is addressed to graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics, and (geometric) quantization.
Operator Structures And Dynamical Systems
DOWNLOAD
Author : Marcel de Jeu
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-11-30
Operator Structures And Dynamical Systems written by Marcel de Jeu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-30 with Mathematics categories.
This volume contains the proceedings of a Leiden Workshop on Dynamical Systems and their accompanying Operator Structures which took place at the Lorentz Center in Leiden, The Netherlands, on July 21-25, 2008. These papers offer a panorama of selfadjoint and non-selfadjoint operator algebras associated with both noncommutative and commutative (topological) dynamical systems and related subjects. Papers on general theory, as well as more specialized ones on symbolic dynamics and complex dynamical systems, are included.
Dynamical Systems Iv
DOWNLOAD
Author : V.I. Arnol'd
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Dynamical Systems Iv written by V.I. Arnol'd and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
From the reviews of the first edition:"... Here ... a wealth of material is displayed for us, too much to even indicate in a review. ... Your reviewer was very impressed by the contents of both volumes (EMS 2 and 4), recommending them without any restriction." Mededelingen van het Wiskundig genootshap 1992
Dynamical Systems Iv
DOWNLOAD
Author : S.P. Novikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-20
Dynamical Systems Iv written by S.P. Novikov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-20 with Mathematics categories.
From the reviews of the first edition:"... Here ... a wealth of material is displayed for us, too much to even indicate in a review. ... Your reviewer was very impressed by the contents of both volumes (EMS 2 and 4), recommending them without any restriction." Mededelingen van het Wiskundig genootshap 1992
Algebraic Integrability Of Nonlinear Dynamical Systems On Manifolds
DOWNLOAD
Author : A.K. Prykarpatsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09
Algebraic Integrability Of Nonlinear Dynamical Systems On Manifolds written by A.K. Prykarpatsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Science categories.
In recent times it has been stated that many dynamical systems of classical mathematical physics and mechanics are endowed with symplectic structures, given in the majority of cases by Poisson brackets. Very often such Poisson structures on corresponding manifolds are canonical, which gives rise to the possibility of producing their hidden group theoretical essence for many completely integrable dynamical systems. It is a well understood fact that great part of comprehensive integrability theories of nonlinear dynamical systems on manifolds is based on Lie-algebraic ideas, by means of which, in particular, the classification of such compatibly bi Hamiltonian and isospectrally Lax type integrable systems has been carried out. Many chapters of this book are devoted to their description, but to our regret so far the work has not been completed. Hereby our main goal in each analysed case consists in separating the basic algebraic essence responsible for the complete integrability, and which is, at the same time, in some sense universal, i. e. , characteristic for all of them. Integrability analysis in the framework of a gradient-holonomic algorithm, devised in this book, is fulfilled through three stages: 1) finding a symplectic structure (Poisson bracket) transforming an original dynamical system into a Hamiltonian form; 2) finding first integrals (action variables or conservation laws); 3) defining an additional set of variables and some functional operator quantities with completely controlled evolutions (for instance, as Lax type representation).