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

- 312 Want to read
- 34 Currently reading

Published
**April 26, 2000** by Springer .

Written in

- 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 | |
---|---|

Format | Paperback |

Number of Pages | 153 |

ID Numbers | |

Open Library | OL9063269M |

ISBN 10 | 3540671617 |

ISBN 10 | 9783540671619 |

SIAM Journal on Applied Dynamical Systems , Abstract | PDF ( KB) () A BIFURCATION ANALYSIS OF A 3D BLOWFLY MODEL IN DISCRETE AND CONTINUOUS by: In computational mathematics, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical gh computer algebra could be considered a subfield of scientific computing, they are generally considered as distinct.

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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 Computer Algebra Methods for Equivariant Dynamical Systems book 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: Gatermann K.

() Symmetric bifurcation theory. In: Gatermann K. (eds) Computer Algebra Methods for Equivariant Dynamical Systems. Lecture Notes in Mathematics, vol Author: Karin Gatermann. The book is also accessible as a self-study text for anyone who has completed two terms of calculus, including highly motivated high school students.

Graduate students preparing to take courses in dynamical systems theory will also find this text useful. 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 ComputationCited 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. Controlled and conditioned invariance for polynomial and rational feedback systems Inproceedings.

In: Advances in Delays and Dynamics, Algebraic and Symbolic Computation Methods in Dynamical Systems,(To appear). BibTeX. Abstract. Computer algebra is a relatively young but rapidly growing field. In this introductory note to the mini-symposium on computer algebra organized as part of the third European Congress of Mathematics, I will not even attempt to address all major streams of research and the many applications of computer by: 1.

On the other hand, the numerical problems in dynamical systems theory have often influenced developments in numerical linear algebra and in numerical analysis; cf.

the books [75], [76], [], [], []. Another link is with software development. The only realistic way to make numerical methods widely available is to include them in software. Get online AudioBook Dynamical Systems and Control (Stability and Control: Theory Methods and Applications) ad Best audioBook AudioBook Dynamical Systems and Control (Stability and Control: Theory Methods and Applications), Download Online AudioBook Dynamical Systems and Control (Stability and Control: Theory Methods and.

I am looking for a textbook or a good source that could help me with dynamical systems. What I mean is an introductory book for it. For example I have enjoyed Real Mathematical Analysis by C.C.

Pugh. I would greatly appreciate if someone could introduce me a book that could put everything about dynamical systems in perspective as good as it has. Since the first edition of this book was published inMaple™ has evolved from Maple V into Maple Accordingly, this new edition has been thoroughly updated and expanded to include more applications, examples, and exercises, all with solutions; two new chapters on neural networks and simulation have also been added.

Is devoted to the theory of symmetry-based dynamics and its application to model and analyze complex systems; Presents complex systems with symmetry in a wide variety of fields, including magnetic and electric field sensors, communication networks, gyroscopes for navigation and underwater vehicle dynamics, energy harvesting, nano oscillators, and precision timing devices.

This is the internet version of Invitation to Dynamical Systems. Unfortunately, the original publisher has let this book go out of print. The version you are now reading is pretty close to the original version (some formatting has changed, so page numbers are unlikely to be the same, and the fonts are diﬀerent).

This book presents a collection of exercises on dynamical systems, modelling and control. Each topic covered includes a summary of the theoretical background, problems with solutions, and further exercises. Topics covered include: block diagram algebra and system transfer functions; mathematical models; analysis of continuous systems in the time domain; root locus analysis; frequency domain Cited by: 3.

These are based on the Routh-Lyapunov method [Lyapunov, ] and some its modifications [Irtegov and Titorenko, ] as well as computer algebra methods [Cox, Little, and O'Shea, ]. In the.Get this from a library!

Computational invariant theory. [Harm Derksen; Gregor Kemper] -- "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.

Equivariant dynamical systems are dynamical systems that have symmetries. A symmetry of a dynamical system is a transformation that takes solutions to solutions.

The equations describing a physical or biological system may have symmetries as a result of the system geometry, modeling assumptions, and/or simplifying normal form transformations.