Computer Algebra Methods For Equivariant Dynamical Systems

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Computer Algebra Methods for Equivariant Dynamical Systems

Karin Gatermann
Computer Algebra Methods for Equivariant Dynamical Systems Book PDF

Author : Karin Gatermann
Publisher : Springer
Page : 163 pages
File Size : 43,8 Mb
Release : 2007-05-06
Category : Mathematics
ISBN : 9783540465195

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Computer Algebra Methods for Equivariant Dynamical Systems by Karin Gatermann Pdf

This book starts with an overview of the research of Gröbner bases which have many applications in various areas of mathematics since they are a general tool for the investigation of polynomial systems. The next chapter describes algorithms in invariant theory including many examples and time tables. These techniques are applied in the chapters on symmetric bifurcation theory and equivariant dynamics. This combination of different areas of mathematics will be interesting to researchers in computational algebra and/or dynamics.

Algebraic and Symbolic Computation Methods in Dynamical Systems

Alban Quadrat,Eva Zerz
Algebraic and Symbolic Computation Methods in Dynamical Systems Book PDF

Author : Alban Quadrat,Eva Zerz
Publisher : Springer Nature
Page : 320 pages
File Size : 55,8 Mb
Release : 2020-05-30
Category : Science
ISBN : 9783030383565

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Algebraic and Symbolic Computation Methods in Dynamical Systems by Alban Quadrat,Eva Zerz Pdf

This book aims at reviewing recent progress in the direction of algebraic and symbolic computation methods for functional systems, e.g. ODE systems, differential time-delay equations, difference equations and integro-differential equations. In the nineties, modern algebraic theories were introduced in mathematical systems theory and in control theory. Combined with real algebraic geometry, which was previously introduced in control theory, the past years have seen a flourishing development of algebraic methods in control theory. One of the strengths of algebraic methods lies in their close connections to computations. The use of the above-mentioned algebraic theories in control theory has been an important source of motivation to develop effective versions of these theories (when possible). With the development of computer algebra and computer algebra systems, symbolic methods for control theory have been developed over the past years. The goal of this book is to propose a partial state of the art in this direction. To make recent results more easily accessible to a large audience, the chapters include materials which survey the main mathematical methods and results and which are illustrated with explicit examples.

Computer Algebra Handbook

Johannes Grabmeier,Erich Kaltofen,Volker Weispfenning
Computer Algebra Handbook Book PDF

Author : Johannes Grabmeier,Erich Kaltofen,Volker Weispfenning
Publisher : Springer Science & Business Media
Page : 656 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642558269

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Computer Algebra Handbook by Johannes Grabmeier,Erich Kaltofen,Volker Weispfenning Pdf

This Handbook gives a comprehensive snapshot of a field at the intersection of mathematics and computer science with applications in physics, engineering and education. Reviews 67 software systems and offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education.

Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

Bernold Fiedler
Ergodic Theory Analysis and Efficient Simulation of Dynamical Systems Book PDF

Author : Bernold Fiedler
Publisher : Springer Science & Business Media
Page : 840 pages
File Size : 49,8 Mb
Release : 2001
Category : Mathematics
ISBN : 3540412905

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Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems by Bernold Fiedler Pdf

This book summarizes and highlights progress in Dynamical Systems achieved during six years of the German Priority Research Program "Ergotic Theory, Analysis, and Efficient Simulation of Dynamical Systems", funded by the Deutsche Forschungsgemeinschaft (DFG). The three fundamental topics of large time behavior, dimension, and measure are tackled with by a rich circle of uncompromisingly rigorous mathematical concepts. The range of applied issues comprises such diverse areas as crystallization and dendrite growth, the dynamo effect, efficient simulation of biomolecules, fluid dynamics and reacting flows, mechanical problems involving friction, population biology, the spread of infectious diseases, and quantum chaos. The surveys in the book are addressed to experts and non-experts in the mathematical community alike. In addition they intend to convey the significance of the results for applications fair into the neighboring disciplines of Science.

Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems

Heinz Hanßmann
Local and Semi Local Bifurcations in Hamiltonian Dynamical Systems Book PDF

Author : Heinz Hanßmann
Publisher : Springer
Page : 248 pages
File Size : 41,9 Mb
Release : 2006-10-18
Category : Mathematics
ISBN : 9783540388968

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Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems by Heinz Hanßmann Pdf

This book demonstrates that while elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Therefore, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system, absent untypical conditions or external parameters. The text moves logically from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations must be replaced by Cantor sets.

Attractivity and Bifurcation for Nonautonomous Dynamical Systems

Martin Rasmussen
Attractivity and Bifurcation for Nonautonomous Dynamical Systems Book PDF

Author : Martin Rasmussen
Publisher : Springer Science & Business Media
Page : 222 pages
File Size : 53,8 Mb
Release : 2007-06-08
Category : Mathematics
ISBN : 9783540712244

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Attractivity and Bifurcation for Nonautonomous Dynamical Systems by Martin Rasmussen Pdf

Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity. It is shown that these notions lead to nonautonomous Morse decompositions.

Normal Forms and Unfoldings for Local Dynamical Systems

James Murdock
Normal Forms and Unfoldings for Local Dynamical Systems Book PDF

Author : James Murdock
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 47,7 Mb
Release : 2006-04-10
Category : Mathematics
ISBN : 9780387217857

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Normal Forms and Unfoldings for Local Dynamical Systems by James Murdock Pdf

This is the most thorough treatment of normal forms currently existing in book form. There is a substantial gap between elementary treatments in textbooks and advanced research papers on normal forms. This book develops all the necessary theory 'from scratch' in just the form that is needed for the application to normal forms, with as little unnecessary terminology as possible.

Symbolic Computation

Ams-IMS-Siam Joint Summer Research Conference on Symbolic Computation Solving Equations I,Ams-Ims-Siam Joint Summer Research Conference on Symbolic Computation
Symbolic Computation Book PDF

Author : Ams-IMS-Siam Joint Summer Research Conference on Symbolic Computation Solving Equations I,Ams-Ims-Siam Joint Summer Research Conference on Symbolic Computation
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 49,8 Mb
Release : 2001
Category : Mathematics
ISBN : 9780821826799

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Symbolic Computation by Ams-IMS-Siam Joint Summer Research Conference on Symbolic Computation Solving Equations I,Ams-Ims-Siam Joint Summer Research Conference on Symbolic Computation Pdf

This volume contains papers related to the research conference, 'Symbolic Computation: Solving Equations in Algebra, Analysis, and Engineering', held at Mount Holyoke College (MA). It provides a broad range of active research areas in symbolic computation as it applies to the solution of polynomial systems. The conference brought together pure and applied mathematicians, computer scientists, and engineers, who use symbolic computation to solve systems of equations or who develop the theoretical background and tools needed for this purpose. Within this general framework, the conference focused on several themes: systems of polynomials, systems of differential equations, non commutative systems, and applications.

Computational Invariant Theory

Harm Derksen,Gregor Kemper
Computational Invariant Theory Book PDF

Author : Harm Derksen,Gregor Kemper
Publisher : Springer
Page : 366 pages
File Size : 54,9 Mb
Release : 2015-12-23
Category : Mathematics
ISBN : 9783662484227

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Computational Invariant Theory by Harm Derksen,Gregor Kemper Pdf

This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be of more than passing interest. More than ten years after the first publication of the book, the second edition now provides a major update and covers many recent developments in the field. Among the roughly 100 added pages there are two appendices, authored by Vladimi r Popov, and an addendum by Norbert A'Campo and Vladimir Popov.

Algorithmic and Quantitative Real Algebraic Geometry

Saugata Basu,Laureano González-Vega
Algorithmic and Quantitative Real Algebraic Geometry Book PDF

Author : Saugata Basu,Laureano González-Vega
Publisher : American Mathematical Soc.
Page : 238 pages
File Size : 55,5 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 0821871021

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Algorithmic and Quantitative Real Algebraic Geometry by Saugata Basu,Laureano González-Vega Pdf

Algorithmic and quantitative aspects in real algebraic geometry are becoming increasingly important areas of research because of their roles in other areas of mathematics and computer science. The papers in this volume collectively span several different areas of current research. The articles are based on talks given at the DIMACS Workshop on ''Algorithmic and Quantitative Aspects of Real Algebraic Geometry''. Topics include deciding basic algebraic properties of real semi-algebraic sets, application of quantitative results in real algebraic geometry towards investigating the computational complexity of various problems, algorithmic and quantitative questions in real enumerative geometry, new approaches towards solving decision problems in semi-algebraic geometry, as well as computing algebraic certificates, and applications of real algebraic geometry to concrete problems arising in robotics and computer graphics. The book is intended for researchers interested in computational methods in algebra.

Bifurcations in Hamiltonian Systems

Henk Broer,Igor Hoveijn,Gerton Lunter,Gert Vegter
Bifurcations in Hamiltonian Systems Book PDF

Author : Henk Broer,Igor Hoveijn,Gerton Lunter,Gert Vegter
Publisher : Springer
Page : 178 pages
File Size : 45,8 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 9783540363989

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Bifurcations in Hamiltonian Systems by Henk Broer,Igor Hoveijn,Gerton Lunter,Gert Vegter Pdf

The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems. They restrict themselves to the case were the following simplification is possible. Near the equilibrium or (quasi-) periodic solution under consideration the linear part allows approximation by a normalized Hamiltonian system with a torus symmetry. It is assumed that reduction by this symmetry leads to a system with one degree of freedom. The volume focuses on two such reduction methods, the planar reduction (or polar coordinates) method and the reduction by the energy momentum mapping. The one-degree-of-freedom system then is tackled by singularity theory, where computer algebra, in particular, Gröbner basis techniques, are applied. The readership addressed consists of advanced graduate students and researchers in dynamical systems.

Imperfect Bifurcation in Structures and Materials

Kiyohiro Ikeda,Kazuo Murota
Imperfect Bifurcation in Structures and Materials Book PDF

Author : Kiyohiro Ikeda,Kazuo Murota
Publisher : Springer Nature
Page : 590 pages
File Size : 52,8 Mb
Release : 2019-09-25
Category : Science
ISBN : 9783030214739

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Imperfect Bifurcation in Structures and Materials by Kiyohiro Ikeda,Kazuo Murota Pdf

Most physical systems lose or gain stability through bifurcation behavior. This book explains a series of experimentally found bifurcation phenomena by means of the methods of static bifurcation theory.

Open Quantum Systems III

Stéphane Attal,Alain Joye,claude-alain pillet
Open Quantum Systems III Book PDF

Author : Stéphane Attal,Alain Joye,claude-alain pillet
Publisher : Springer
Page : 314 pages
File Size : 52,6 Mb
Release : 2006-08-18
Category : Mathematics
ISBN : 9783540339670

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Open Quantum Systems III by Stéphane Attal,Alain Joye,claude-alain pillet Pdf

This volume is the third and last of a series devoted to the lecture notes of the Grenoble Summer School on “Open Quantum Systems” which took place at the th th Institut Fourier from June 16 to July 4 2003. The contributions presented in this volumecorrespondtoexpanded versionsofthelecturenotesprovidedbytheauthors to the students of the Summer School. The corresponding lectures were scheduled in the last part of the School devoted to recent developments in the study of Open Quantum Systems. Whereas the rst two volumes were dedicated to a detailed exposition of the mathematical techniques and physical concepts relevant in the study of Open S- tems with noapriori pre-requisites, the contributions presented in this volume request from the reader some familiarity with these aspects. Indeed, the material presented here aims at leading the reader already acquainted with the basics in ? quantum statistical mechanics, spectral theory of linear operators,C -dynamical systems, and quantum stochastic differential equations to the front of the current research done on various aspects of Open Quantum Systems. Nevertheless, pe- gogical efforts have been made by the various authors of these notes so that this volume should be essentially self-contained for a reader with minimal previous - posure to the themes listed above. In any case, the reader in need of complements can always turn to these rst two volumes. The topics covered in these lectures notes start with an introduction to n- equilibrium quantum statistical mechanics.

Foundations of Computational Mathematics, Budapest 2011

Society for the Foundation of Computational Mathematics
Foundations of Computational Mathematics Budapest 2011 Book PDF

Author : Society for the Foundation of Computational Mathematics
Publisher : Cambridge University Press
Page : 249 pages
File Size : 49,7 Mb
Release : 2013
Category : Computers
ISBN : 9781107604070

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Foundations of Computational Mathematics, Budapest 2011 by Society for the Foundation of Computational Mathematics Pdf

A diverse collection of articles by leading experts in computational mathematics, written to appeal to established researchers and non-experts.

European Congress of Mathematics

Carles Casacuberta,Rosa M. Miro-Roig,Joan Verdera,Sebastia Xambo-Descamps
European Congress of Mathematics Book PDF

Author : Carles Casacuberta,Rosa M. Miro-Roig,Joan Verdera,Sebastia Xambo-Descamps
Publisher : Birkhäuser
Page : 630 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882668

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European Congress of Mathematics by Carles Casacuberta,Rosa M. Miro-Roig,Joan Verdera,Sebastia Xambo-Descamps Pdf

This is the second volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician.