Structure Of Dynamical Systems
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Structure Of Dynamical Systems
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Author : J.M. Souriau
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-09-23
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 1997-09-23 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.
Structure Of Dynamical Systems Structure Des Systemes Dynamiques
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Author : Jean-Marie Souriau
language : en
Publisher:
Release Date : 1997
Structure Of Dynamical Systems Structure Des Systemes Dynamiques written by Jean-Marie Souriau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
Structure Of Dynamical Systems
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Author : J.M. Souriau
language : en
Publisher: Birkhäuser
Release Date : 1997-09-23
Structure Of Dynamical Systems written by J.M. Souriau and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-09-23 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.
Algebraic Structure Of Dynamical Systems
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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.
The Structure Of Attractors In Dynamical Systems
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Author : N. G. Markley
language : en
Publisher:
Release Date : 2014-01-15
The Structure Of Attractors In Dynamical Systems written by N. G. Markley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Lectures On Dynamical Systems Structural Stability And Their Applications
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Author : Kotik K Lee
language : en
Publisher: World Scientific
Release Date : 1992-05-14
Lectures On Dynamical Systems Structural Stability And Their Applications written by Kotik K Lee and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-05-14 with Mathematics categories.
The communication of knowledge on nonlinear dynamical systems, between the mathematicians working on the analytic approach and the scientists working mostly on the applications and numerical simulations has been less than ideal. This volume hopes to bridge the gap between books written on the subject by mathematicians and those written by scientists. The second objective of this volume is to draw attention to the need for cross-fertilization of knowledge between the physical and biological scientists. The third aim is to provide the reader with a personal guide on the study of global nonlinear dynamical systems.
The Structure Of Dynamical Systems
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Author : 角谷静夫
language : ja
Publisher:
Release Date : 1972
The Structure Of Dynamical Systems written by 角谷静夫 and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.
Dynamical Systems Iv
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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: "... In general the articles ... are well written in a style that enables one to grasp the ideas. The actual style is a readable mix of the important results, outlines of proofs and complete proofs when it does not take too long together with readable explanations of what is going on. Also very useful are the large lists of references which are important not only for their mathematical content but also because the references given also contain articles in the Soviet literature which may not be familiar or possibly accessible to readers." New Zealand Math. Soc. Newsletter 1991 "... 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. As far as he could judge, most presentations seem fairly complete..." Mededelingen van het Wiskundig genootshap 1992
Differentiable Dynamical Systems
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Author : Lan Wen
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-07-20
Differentiable Dynamical Systems written by Lan Wen 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 2016-07-20 with Mathematics categories.
This is a graduate text in differentiable dynamical systems. It focuses on structural stability and hyperbolicity, a topic that is central to the field. Starting with the basic concepts of dynamical systems, analyzing the historic systems of the Smale horseshoe, Anosov toral automorphisms, and the solenoid attractor, the book develops the hyperbolic theory first for hyperbolic fixed points and then for general hyperbolic sets. The problems of stable manifolds, structural stability, and shadowing property are investigated, which lead to a highlight of the book, the Ω-stability theorem of Smale. While the content is rather standard, a key objective of the book is to present a thorough treatment for some tough material that has remained an obstacle to teaching and learning the subject matter. The treatment is straightforward and hence could be particularly suitable for self-study. Selected solutions are available electronically for instructors only. Please send email to [email protected] for more information.
International Symposium On Mathematical Theory Of Networks And Systems
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Author : International Symposium on Mathematical Theory of Networks and Systems
language : en
Publisher:
Release Date : 1979
International Symposium On Mathematical Theory Of Networks And Systems written by International Symposium on Mathematical Theory of Networks and Systems and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Electric networks categories.