Last edited by Tarr
Monday, July 13, 2020 | History

7 edition of Computer Algebra Methods for Equivariant Dynamical Systems found in the catalog.

Computer Algebra Methods for Equivariant Dynamical Systems

by Karin Gatermann

  • 121 Want to read
  • 8 Currently reading

Published by Springer .
Written in English

    Subjects:
  • Mathematical theory of computation,
  • Mathematics for scientists & engineers,
  • Science/Mathematics,
  • Differentiable dynamical syste,
  • Computer Mathematics,
  • Mathematics,
  • Grèobner bases,
  • Differential Equations,
  • Applied,
  • Computer Science,
  • Computers-Computer Science,
  • Gröbner bases,
  • Mathematics / Applied,
  • Mathematics / Differential Equations,
  • Mathematics-Applied,
  • dynamical systems,
  • invariant theory,
  • Algebra,
  • Data processing,
  • Differentiable Dynamical Systems,
  • Grobner bases

  • Edition Notes

    Lecture Notes in Mathematics

    The Physical Object
    FormatPaperback
    Number of Pages153
    ID Numbers
    Open LibraryOL9063269M
    ISBN 103540671617
    ISBN 109783540671619

    Invariant theory and reversible-equivariant vector fields Article in Journal of Pure and Applied Algebra (5) May with 39 Reads How we measure 'reads'. In this book ths author has done a fine job of overviewing the subject of dynamical systems, particularly with regards to systems that exhibit chaotic behavior. There are illustrations given in the book, and they effectively assist in the understanding of a sometimes abstract subject/5(4).

    Computer Algebra Methods for Equivariant Dynamical Systems, () Polynomial Systems from Certain Differential Equations. Journal of Symbolic Computation , Cited by: System Upgrade on Feb 12th During this period, E-commerce and registration of new users may not be available for up to 12 hours. For online purchase, please visit .

    In this book we intend to explore some topics on dynamical systems, using an active teaching approach, supported by computing tools and trying to avoid too may abstract details. The use of a Computer Algebra System (CAS) does not eliminate the need for mathematical analysis from the student; using a CAS to teach an engineering course does. This book represents a significant advance for degree theory in the equivariant setting; that is, to systems of equations with symmetry. For example, it introduces the notion of G-equivariant twisted degree, which is essential for the study of equivariant Hopf bifurcations of dynamical systems.


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Computer Algebra Methods for Equivariant Dynamical Systems by Karin Gatermann Download PDF EPUB FB2

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 : Springer-Verlag Berlin Heidelberg.

Computer algebra methods for equivariant dynamical systems. Berlin ; New York: Springer, © (DLC) (OCoLC) Material Type: Document, Internet resource: Document Type: Internet Resource, Computer File: All Authors / Contributors: Karin Gatermann.

Get this from a library. Computer algebra methods for equivariant dynamical systems. [Karin Gatermann]. Dynamic Buchberger algorithm 39 Elimination 42 2. Algorithms for the computation of invariants and equivariants 47 Using the Hilbert series 47 Invariants 48 Equivariants 59 Using the nullcone 67 Using a homogeneous System of parameters 73 Computing uniqueness 85 3.

Symmetrie bifurcation theory Computer Algebra Methods for Equivariant Dynamical Systems. Cached. Download Links [] Save to List; Add to Collection @MISC{Gatermann_computeralgebra, author = {Karin Gatermann}, title = {Computer Algebra Methods for Equivariant Dynamical Keyphrases.

equivariant dynamical system computer algebra method. 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 dynamicsAuthor: Karin Gatermann.

Download PDF: Sorry, we are unable to provide the full text but you may find it at the following location(s): (external link) http Author: Karin Gatermann.

Gatermann K. () Algorithms for the computation of invariants and equivariants. In: Gatermann K. (eds) Computer Algebra Methods for Equivariant Dynamical Systems. Lecture Notes in Mathematics, vol Author: Karin Gatermann. 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. Mathematica, Maple, and similar software packages provide programs that carry out sophisticated mathematical operations. Applying the ideas introduced in Computer Algebra and Symbolic Computation: Elementary Algorithms, this book explores the application of algorithms to such methods as automatic simplification, polynomial decomposition, and polynomial by: For an introduction to the problems and methods of dynamical systems invariant under a symmetry group one may consult [1,9, 2], while in [10] an exposition is given of the topological properties.

I currently have the book Dynamical Systems with Applications Using Mathematica by Stephen Lynch. I used it in an undergrad introductory course for dynamical systems, but it's extremely terse. As an example, one section of the book dropped the term 'manifold' at one point without giving a.

With these tools at hand, we show how computer algebra can be applied to investigate the accessibility and observability problem for this system class.

The contribution is organized as follows: in Section 2 we consider dynamical systems and give a geometric description in the notation of jet bundles and introduce the issue of formal by: 2. The book has two aims.

One is to expound the mathematical methods of equivariant bifurcation theory. Beyond the classical bifurcation tools, such as center manifold and normal form reductions, the presence of symmetry requires the introduction of the algebraic.

The favorable reaction to the first edition of this book confirmed that the publication of such an application-oriented text on bifurcation theory of dynamical systems was well timed. The selected topics indeed cover ma-jor practical issues of applying the bifurcation theory to finite-dimensional problems.

Dynamical systems Chapter 6. Dynamical systems § Dynamical systems § The flow of an autonomous equation § Orbits and invariant sets § The Poincar´e map § Stability of fixed points § Stability via Liapunov’s method § Newton’s equation in one dimension Chapter 7.

Planar. "The book will be useful for all kinds of dynamical systems courses. [It] shows the power of using a computer algebra program to study dynamical systems, and, by giving so many worked examples, provides ample opportunity for experiments.

[It] is well written and a pleasure to read, which is helped by its attention to historical background."5/5(6). this textbook.

This book can therefore serve as a springboard for those stu-dents interested in continuing their study of ordinary differential equations and dynamical systems and doing research in these areas. Chapter 3 ends with a technique for constructing the global phase portrait of a dynami-cal system.

Computer Algebra Methods for Equivariant Dynamical Systems. Gatermann K. () Gröbner bases. In: Gatermann K. (eds) Computer Algebra Methods for Equivariant Dynamical Systems. Lecture Notes in Mathematics, vol Springer, Berlin, Heidelberg. First. This book represents a significant advance for degree theory in the equivariant setting; that is, to systems of equations with symmetry.

For example, it introduces the notion of G-equivariant twisted degree, which is essential for the study of equivariant Hopf bifurcations of dynamical by:. Geometric Methods for Discrete Dynamical Systems (Oxford Engineering Science Series) Geometric Methods for Discrete Dynamical Systems (Oxford Engineering Science Series) [PDF] Computer Algebra Methods for Equivariant Dynamical Systems (Lecture Notes in Mathematics) - Removed.Figure The solution graphs and phase line for x = ax for a First-Order Equations.

by a solid dot), while any other solution moves up or down the x-axis, as indicated by the arrows in Figure The equation x = ax is stable in a certain sense if a = 0.The author focuses on the description of numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems.

This subfield has the particular attraction of having links with the geometric theory of differential equations, numerical analysis, and linear by: