Simplicial Dynamical Systems

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Simplicial Dynamical Systems

Author : Ethan Akin
Publisher : American Mathematical Soc.
Page : 197 pages
File Size : 45,5 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821813836

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Simplicial Dynamical Systems by Ethan Akin Pdf

Abstract A - simplicial dynamical system is a simplicial map $g:K^* \rightarrow K$ where $K$ is a finite simplicial complex triangulating a compact polyhedron $X$ and $K^*$ is a proper subdivision of $K$, e.g. the barycentric or any further subdivision. The dynamics of the associated piecewise linear map $g: X X$ can be analyzed by using certain naturally related subshifts of finite type. Any continuous map on $X$ can be $C^0$ approximated by such systems. Other examples yield interesting subshift constructions.

Simplicial Dynamical Systems

Author : Ethan Akin
Publisher : American Mathematical Society(RI)
Page : 197 pages
File Size : 48,5 Mb
Release : 2014-09-11
Category : Differentiable dynamical systems
ISBN : 1470402580

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Simplicial Dynamical Systems by Ethan Akin Pdf

A simplicial dynamical system is a simplicial map $g: K DEGREES* \rightarrow K$ where $K$ is a finite simplicial complex triangulating a compact polyhedron $X$ and $K DEGREES*$ is a proper subdivision of $K$, for example, the barycentric or any further subdivision. the dynamics of the asociated piecewise linear map $g: X X$ can be analyzed by using certain naturally related subshifts of finite type. Any continous map on $X$ can be $C DEGREES0$ approximated by such systems. Other examples yield interesting

Introduction to the Modern Theory of Dynamical Systems

Author : Anatole Katok,A. B. Katok,Boris Hasselblatt
Publisher : Cambridge University Press
Page : 828 pages
File Size : 55,9 Mb
Release : 1995
Category : Mathematics
ISBN : 0521575575

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Introduction to the Modern Theory of Dynamical Systems by Anatole Katok,A. B. Katok,Boris Hasselblatt Pdf

This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up.

Simplicial Complexes In Complex Systems: In Search For Alternatives

Author : Yi Zhao,Slobodan Maletic
Publisher : World Scientific
Page : 149 pages
File Size : 41,5 Mb
Release : 2021-05-25
Category : Mathematics
ISBN : 9789811226335

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Simplicial Complexes In Complex Systems: In Search For Alternatives by Yi Zhao,Slobodan Maletic Pdf

For the last few decades researchers from different fields gather their findings and knowledge trying to give a shape to the new science of complex systems. To address this problem, new tools and methods have to be established. A new, or more precisely an alternative, framework for the characterization of complex system was proposed. In this book we will introduce the applicability of applicability of simplicial complexes in the science of complex systems. After introducing the main definitions and properties of simplicial complexes necessary for representation and analysis of complex systems, we will illustrate the usefulness and versatility of tools and concepts related to the simplicial complexes.

Control of Uncertain Dynamic Systems

Author : Shankar P. Bhattacharyya,Lee H. Keel
Publisher : CRC Press
Page : 535 pages
File Size : 41,7 Mb
Release : 2020-09-23
Category : Technology & Engineering
ISBN : 9781000102567

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Control of Uncertain Dynamic Systems by Shankar P. Bhattacharyya,Lee H. Keel Pdf

This book is a collection of 34 papers presented by leading researchers at the International Workshop on Robust Control held in San Antonio, Texas in March 1991. The common theme tying these papers together is the analysis, synthesis, and design of control systems subject to various uncertainties. The papers describe the latest results in parametric understanding, H8 uncertainty, l1 optical control, and Quantitative Feedback Theory (QFT). The book is the first to bring together all the diverse points of view addressing the robust control problem and should strongly influence development in the robust control field for years to come. For this reason, control theorists, engineers, and applied mathematicians should consider it a crucial acquisition for their libraries.

Robot Motion and Control 2009

Author : Krzysztof R. Kozlowski
Publisher : Springer Science & Business Media
Page : 490 pages
File Size : 54,8 Mb
Release : 2009-11-15
Category : Technology & Engineering
ISBN : 9781848829848

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Robot Motion and Control 2009 by Krzysztof R. Kozlowski Pdf

Robot Motion Control 2009 presents very recent results in robot motion and control. Forty short papers have been chosen from those presented at the sixth International Workshop on Robot Motion and Control held in Poland in June 2009. The authors of these papers have been carefully selected and represent leading institutions in this field. The following recent developments are discussed: design of trajectory planning schemes for holonomic and nonholonomic systems with optimization of energy, torque limitations and other factors, new control algorithms for industrial robots, nonholonomic systems and legged robots, different applications of robotic systems in industry and everyday life, like medicine, education, entertainment and others, multiagent systems consisting of mobile and flying robots with their applications. The book is suitable for graduate students of automation and robotics, informatics and management, mechatronics, electronics and production engineering systems as well as scientists and researchers working in these fields.

Higher-Order Systems

Author : Federico Battiston,Giovanni Petri
Publisher : Springer Nature
Page : 436 pages
File Size : 52,6 Mb
Release : 2022-04-26
Category : Science
ISBN : 9783030913748

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Higher-Order Systems by Federico Battiston,Giovanni Petri Pdf

The book discusses the potential of higher-order interactions to model real-world relational systems. Over the last decade, networks have emerged as the paradigmatic framework to model complex systems. Yet, as simple collections of nodes and links, they are intrinsically limited to pairwise interactions, limiting our ability to describe, understand, and predict complex phenomena which arise from higher-order interactions. Here we introduce the new modeling framework of higher-order systems, where hypergraphs and simplicial complexes are used to describe complex patterns of interactions among any number of agents. This book is intended both as a first introduction and an overview of the state of the art of this rapidly emerging field, serving as a reference for network scientists interested in better modeling the interconnected world we live in.

Topological Dimension and Dynamical Systems

Author : Michel Coornaert
Publisher : Springer
Page : 233 pages
File Size : 49,9 Mb
Release : 2015-06-20
Category : Mathematics
ISBN : 9783319197944

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Topological Dimension and Dynamical Systems by Michel Coornaert Pdf

Translated from the popular French edition, the goal of the book is to provide a self-contained introduction to mean topological dimension, an invariant of dynamical systems introduced in 1999 by Misha Gromov. The book examines how this invariant was successfully used by Elon Lindenstrauss and Benjamin Weiss to answer a long-standing open question about embeddings of minimal dynamical systems into shifts. A large number of revisions and additions have been made to the original text. Chapter 5 contains an entirely new section devoted to the Sorgenfrey line. Two chapters have also been added: Chapter 9 on amenable groups and Chapter 10 on mean topological dimension for continuous actions of countable amenable groups. These new chapters contain material that have never before appeared in textbook form. The chapter on amenable groups is based on Følner’s characterization of amenability and may be read independently from the rest of the book. Although the contents of this book lead directly to several active areas of current research in mathematics and mathematical physics, the prerequisites needed for reading it remain modest; essentially some familiarities with undergraduate point-set topology and, in order to access the final two chapters, some acquaintance with basic notions in group theory. Topological Dimension and Dynamical Systems is intended for graduate students, as well as researchers interested in topology and dynamical systems. Some of the topics treated in the book directly lead to research areas that remain to be explored.

Computational Models of Complex Systems

Author : Vijay Kumar Mago,Vahid Dabbaghian
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 55,7 Mb
Release : 2013-10-31
Category : Technology & Engineering
ISBN : 9783319012858

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Computational Models of Complex Systems by Vijay Kumar Mago,Vahid Dabbaghian Pdf

Computational and mathematical models provide us with the opportunities to investigate the complexities of real world problems. They allow us to apply our best analytical methods to define problems in a clearly mathematical manner and exhaustively test our solutions before committing expensive resources. This is made possible by assuming parameter(s) in a bounded environment, allowing for controllable experimentation, not always possible in live scenarios. For example, simulation of computational models allows the testing of theories in a manner that is both fundamentally deductive and experimental in nature. The main ingredients for such research ideas come from multiple disciplines and the importance of interdisciplinary research is well recognized by the scientific community. This book provides a window to the novel endeavours of the research communities to present their works by highlighting the value of computational modelling as a research tool when investigating complex systems. We hope that the readers will have stimulating experiences to pursue research in these directions.

Dynamical Systems VII

Author : V.I. Arnol'd,S.P. Novikov
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 53,5 Mb
Release : 2013-12-14
Category : Mathematics
ISBN : 9783662067963

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Dynamical Systems VII by V.I. Arnol'd,S.P. Novikov Pdf

A collection of five surveys on dynamical systems, indispensable for graduate students and researchers in mathematics and theoretical physics. Written in the modern language of differential geometry, the book covers all the new differential geometric and Lie-algebraic methods currently used in the theory of integrable systems.

Dynamical Numbers: Interplay between Dynamical Systems and Number Theory

Author : S. F. Koli︠a︡da
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 42,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821849583

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Dynamical Numbers: Interplay between Dynamical Systems and Number Theory by S. F. Koli︠a︡da Pdf

This volume contains papers from the special program and international conference on Dynamical Numbers which were held at the Max-Planck Institute in Bonn, Germany in 2009. These papers reflect the extraordinary range and depth of the interactions between ergodic theory and dynamical systems and number theory. Topics covered in the book include stationary measures, systems of enumeration, geometrical methods, spectral methods, and algebraic dynamical systems.

Stability Theory of Dynamical Systems

Author : N.P. Bhatia,G.P. Szegö
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 55,5 Mb
Release : 2002-01-10
Category : Science
ISBN : 3540427481

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Stability Theory of Dynamical Systems by N.P. Bhatia,G.P. Szegö Pdf

Reprint of classic reference work. Over 400 books have been published in the series Classics in Mathematics, many remain standard references for their subject. All books in this series are reissued in a new, inexpensive softcover edition to make them easily accessible to younger generations of students and researchers. "... The book has many good points: clear organization, historical notes and references at the end of every chapter, and an excellent bibliography. The text is well-written, at a level appropriate for the intended audience, and it represents a very good introduction to the basic theory of dynamical systems."

Dynamical Systems by Example

Author : Luís Barreira,Claudia Valls
Publisher : Springer
Page : 223 pages
File Size : 50,9 Mb
Release : 2019-04-17
Category : Mathematics
ISBN : 9783030159153

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Dynamical Systems by Example by Luís Barreira,Claudia Valls Pdf

This book comprises an impressive collection of problems that cover a variety of carefully selected topics on the core of the theory of dynamical systems. Aimed at the graduate/upper undergraduate level, the emphasis is on dynamical systems with discrete time. In addition to the basic theory, the topics include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as basic ergodic theory. As in other areas of mathematics, one can gain the first working knowledge of a topic by solving selected problems. It is rare to find large collections of problems in an advanced field of study much less to discover accompanying detailed solutions. This text fills a gap and can be used as a strong companion to an analogous dynamical systems textbook such as the authors’ own Dynamical Systems (Universitext, Springer) or another text designed for a one- or two-semester advanced undergraduate/graduate course. The book is also intended for independent study. Problems often begin with specific cases and then move on to general results, following a natural path of learning. They are also well-graded in terms of increasing the challenge to the reader. Anyone who works through the theory and problems in Part I will have acquired the background and techniques needed to do advanced studies in this area. Part II includes complete solutions to every problem given in Part I with each conveniently restated. Beyond basic prerequisites from linear algebra, differential and integral calculus, and complex analysis and topology, in each chapter the authors recall the notions and results (without proofs) that are necessary to treat the challenges set for that chapter, thus making the text self-contained.

Computer Algebra in Scientific Computing

Author : V.G. Ganzha,E.W. Mayr,E.V. Vorozhtsov
Publisher : Springer
Page : 460 pages
File Size : 54,8 Mb
Release : 2007-09-04
Category : Computers
ISBN : 9783540751878

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Computer Algebra in Scientific Computing by V.G. Ganzha,E.W. Mayr,E.V. Vorozhtsov Pdf

This book constitutes the refereed proceedings of the 10th International Workshop on Computer Algebra in Scientific Computing, CASC 2007, held in Bonn, Germany, in September 2007. The volume is dedicated to Professor Vladimir P. Gerdt on the occasion of his 60th birthday. The papers cover not only various expanding applications of computer algebra to scientific computing but also the computer algebra systems themselves and the CA algorithms.