Isolated Invariant Sets And The Morse Index

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Isolated Invariant Sets and the Morse Index

Author : Charles C. Conley
Publisher : American Mathematical Soc.
ISBN 13 : 0821816888
Total Pages : 102 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Isolated Invariant Sets and the Morse Index by : Charles C. Conley

Download or read book Isolated Invariant Sets and the Morse Index written by Charles C. Conley and published by American Mathematical Soc.. This book was released on 1978-12-31 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lectures from the Conference Board of Mathematical Sciences meeting held at the University of Colorado on May 31-June 4, 1976. The lectures consist of an expository discussion of basic results for topological flows and a somewhat more detailed discussion of isolated invariant sets and continuation. The construction of the index for isolated invariant sets is new and allows more general application than previous ones. Also, the index itself is endowed with more structure and the continuation theorem is modified to take this new structure into account. Some elementary applications are given, but the main emphasis is on the abstract theory.

Isolated Invariant Sets and the Morse Index. (Expository Lectures from the CBMS Regional Conference Held at the Univ. of Colorado, May 31 - June 4, 1976). Publ. by the American Math. Soc

Download Isolated Invariant Sets and the Morse Index. (Expository Lectures from the CBMS Regional Conference Held at the Univ. of Colorado, May 31 - June 4, 1976). Publ. by the American Math. Soc PDF Online Free

Author : Charles Cameron Conley
Publisher :
ISBN 13 : 9780821816882
Total Pages : 89 pages
Book Rating : 4.8/5 (168 download)

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Book Synopsis Isolated Invariant Sets and the Morse Index. (Expository Lectures from the CBMS Regional Conference Held at the Univ. of Colorado, May 31 - June 4, 1976). Publ. by the American Math. Soc by : Charles Cameron Conley

Download or read book Isolated Invariant Sets and the Morse Index. (Expository Lectures from the CBMS Regional Conference Held at the Univ. of Colorado, May 31 - June 4, 1976). Publ. by the American Math. Soc written by Charles Cameron Conley and published by . This book was released on 1978 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Application of the Generalized Morse Index to Travelling Wave Solutions of a Competitive Reaction-Diffusion Model

Author : Charles C. Conley
Publisher :
ISBN 13 :
Total Pages : 43 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis An Application of the Generalized Morse Index to Travelling Wave Solutions of a Competitive Reaction-Diffusion Model by : Charles C. Conley

Download or read book An Application of the Generalized Morse Index to Travelling Wave Solutions of a Competitive Reaction-Diffusion Model written by Charles C. Conley and published by . This book was released on 1980 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: The existence of travelling wave solutions of a diffusion reaction-system is studied via the generalized Morse index of isolated invariant sets. This index theory is analogous to degree theory, and the method of proof follows lines familiar from the latter theory. The equations in question are 'deformed' to a 'standard' system where the index can be easily computed, and the existence theorem follows from the 'non-triviality' of the index. The index theory has been described in other papers; here the main job is to construct 'isolating neighborhoods' which are analogous (in the degree theory) to open sets with no critical points on the boundary. Some novel means of location such neighborhoods are described.

The Homotopy Index and Partial Differential Equations

Author : Krzysztof P. Rybakowski
Publisher : Springer Science & Business Media
ISBN 13 : 3642728332
Total Pages : 217 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis The Homotopy Index and Partial Differential Equations by : Krzysztof P. Rybakowski

Download or read book The Homotopy Index and Partial Differential Equations written by Krzysztof P. Rybakowski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: The homotopy index theory was developed by Charles Conley for two sided flows on compact spaces. The homotopy or Conley index, which provides an algebraic-topologi cal measure of an isolated invariant set, is defined to be the ho motopy type of the quotient space N /N , where is a certain 1 2 1 2 compact pair, called an index pair. Roughly speaking, N1 isolates the invariant set and N2 is the "exit ramp" of N . 1 It is shown that the index is independent of the choice of the in dex pair and is invariant under homotopic perturbations of the flow. Moreover, the homotopy index generalizes the Morse index of a nQnde generate critical point p with respect to a gradient flow on a com pact manifold. In fact if the Morse index of p is k, then the homo topy index of the invariant set {p} is Ik - the homotopy type of the pointed k-dimensional unit sphere.

Topological Methods, Variational Methods and Their Applications

Author : Haim Brzis
Publisher : World Scientific
ISBN 13 : 9812382623
Total Pages : 302 pages
Book Rating : 4.8/5 (123 download)

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Book Synopsis Topological Methods, Variational Methods and Their Applications by : Haim Brzis

Download or read book Topological Methods, Variational Methods and Their Applications written by Haim Brzis and published by World Scientific. This book was released on 2003 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: ICM 2002 Satellite Conference on Nonlinear Analysis was held in the period: August 1418, 2002 at Taiyuan, Shanxi Province, China. This conference was organized by Mathematical School of Peking University, Academy of Mathematics and System Sciences of Chinese Academy of Sciences, Mathematical school of Nankai University, and Department of Mathematics of Shanxi University, and was sponsored by Shanxi Province Education Committee, Tian Yuan Mathematics Foundation, and Shanxi University. 166 mathematicians from 21 countries and areas in the world attended the conference. 53 invited speakers and 30 contributors presented their lectures. This conference aims at an overview of the recent development in nonlinear analysis. It covers the following topics: variational methods, topological methods, fixed point theory, bifurcations, nonlinear spectral theory, nonlinear Schrvdinger equations, semilinear elliptic equations, Hamiltonian systems, central configuration in N-body problems and variational problems arising in geometry and physics.

Polynomial Rings and Affine Spaces

Author : Masayoshi Nagata
Publisher : American Mathematical Soc.
ISBN 13 : 0821838822
Total Pages : 102 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Polynomial Rings and Affine Spaces by : Masayoshi Nagata

Download or read book Polynomial Rings and Affine Spaces written by Masayoshi Nagata and published by American Mathematical Soc.. This book was released on 1978 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains expository lectures from the Conference Board of the Mathematical Sciences Regional Conference held at Northern Illinois University on July 25-29, 1977.

Dynamical Systems

Author : Ludwig Arnold
Publisher : Springer
ISBN 13 : 3540494154
Total Pages : 336 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Dynamical Systems by : Ludwig Arnold

Download or read book Dynamical Systems written by Ludwig Arnold and published by Springer. This book was released on 2006-11-14 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the lecture notes written by the four principal speakers at the C.I.M.E. session on Dynamical Systems held at Montecatini, Italy in June 1994. The goal of the session was to illustrate how methods of dynamical systems can be applied to the study of ordinary and partial differential equations. Topics in random differential equations, singular perturbations, the Conley index theory, and non-linear PDEs were discussed. Readers interested in asymptotic behavior of solutions of ODEs and PDEs and familiar with basic notions of dynamical systems will wish to consult this text.

Differential Equations, Chaos and Variational Problems

Author : Vasile Staicu
Publisher : Springer Science & Business Media
ISBN 13 : 3764384824
Total Pages : 436 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Differential Equations, Chaos and Variational Problems by : Vasile Staicu

Download or read book Differential Equations, Chaos and Variational Problems written by Vasile Staicu and published by Springer Science & Business Media. This book was released on 2008-03-12 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of original articles and surveys written by leading experts in their fields is dedicated to Arrigo Cellina and James A. Yorke on the occasion of their 65th birthday. The volume brings the reader to the border of research in differential equations, a fast evolving branch of mathematics that, besides being a main subject for mathematicians, is one of the mathematical tools most used both by scientists and engineers.

Structural Stability, the Theory of Catastrophes, and Applications in the Sciences

Author : P. Hilton
Publisher : Springer
ISBN 13 : 3540382542
Total Pages : 415 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Structural Stability, the Theory of Catastrophes, and Applications in the Sciences by : P. Hilton

Download or read book Structural Stability, the Theory of Catastrophes, and Applications in the Sciences written by P. Hilton and published by Springer. This book was released on 2006-11-14 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a progress report on an experimental program, begun a year ago, in the exploration of resonant furcations (= catastrophes) by analog simulation and direct observation - the macroscope program.

Handbook of Dynamical Systems

Author : B. Fiedler
Publisher : Gulf Professional Publishing
ISBN 13 : 0080532845
Total Pages : 1099 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Dynamical Systems by : B. Fiedler

Download or read book Handbook of Dynamical Systems written by B. Fiedler and published by Gulf Professional Publishing. This book was released on 2002-02-21 with total page 1099 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others. While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to namejust a few, are ubiquitous dynamical concepts throughout the articles.

Dynamics of Infinite Dimensional Systems

Author : Shui-Nee Chow
Publisher : Springer Science & Business Media
ISBN 13 : 3642864589
Total Pages : 509 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Dynamics of Infinite Dimensional Systems by : Shui-Nee Chow

Download or read book Dynamics of Infinite Dimensional Systems written by Shui-Nee Chow and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 1986 NATO Advanced Study Insti tute on Dynamics of Infini te Dimensional Systems was held at the Instituto Superior Tecnico. Lisbon. Portugal. In recent years. there have been several research workers who have been considering partial differential equations and functional differential equations as dynamical systems on function spaces. Such approaches have led to the formulation of more theoretical problems that need to be investigated. In the applications. the theoretical ideas have contributed significantly to a better understanding of phenomena that have been experimentally and computationally observed. The investigators of this development come wi th several different backgrounds - some from classical partial differential equations. some from classical ordinary differential equations and some interested in specific applications. Each group has special ideas and often these ideas have not been transmitted from one group to another. The purpose of this NATO Workshop was to bring together research workers from these various areas. It provided asoundboard for the impact of the ideas of each respective discipline. We believe that goal was accomplished. but time will be a better judge. We have included the list of participants at the workshop. with most of these giving a presentation. Although the proceedings do not include all of the presentations. it is a good representative sampie. We wish to express our gratitude to NATO. and.to Dr. M. di Lullo of NATO. who unfortunately did not live to see the completion of this project.

Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology

Author : Paul Biran
Publisher : Springer Science & Business Media
ISBN 13 : 1402042663
Total Pages : 476 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology by : Paul Biran

Download or read book Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology written by Paul Biran and published by Springer Science & Business Media. This book was released on 2006-02-12 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers collected in this volume are contributions to the 43rd session of the Seminaire ́ de mathematiques ́ superieures ́ (SMS) on “Morse Theoretic Methods in Nonlinear Analysis and Symplectic Topology.” This session took place at the Universite ́ de Montreal ́ in July 2004 and was a NATO Advanced Study Institute (ASI). The aim of the ASI was to bring together young researchers from various parts of the world and to present to them some of the most signi cant recent advances in these areas. More than 77 mathematicians from 17 countries followed the 12 series of lectures and participated in the lively exchange of ideas. The lectures covered an ample spectrum of subjects which are re ected in the present volume: Morse theory and related techniques in in nite dim- sional spaces, Floer theory and its recent extensions and generalizations, Morse and Floer theory in relation to string topology, generating functions, structure of the group of Hamiltonian di?eomorphisms and related dynamical problems, applications to robotics and many others. We thank all our main speakers for their stimulating lectures and all p- ticipants for creating a friendly atmosphere during the meeting. We also thank Ms. Diane Belanger ́ , our administrative assistant, for her help with the organi- tion and Mr. Andre ́ Montpetit, our technical editor, for his help in the preparation of the volume.

Shock Waves and Reaction—Diffusion Equations

Author : Joel Smoller
Publisher : Springer Science & Business Media
ISBN 13 : 1468401521
Total Pages : 596 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Shock Waves and Reaction—Diffusion Equations by : Joel Smoller

Download or read book Shock Waves and Reaction—Diffusion Equations written by Joel Smoller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: . . . the progress of physics will to a large extent depend on the progress of nonlinear mathe matics, of methods to solve nonlinear equations . . . and therefore we can learn by comparing different nonlinear problems. WERNER HEISENBERG I undertook to write this book for two reasons. First, I wanted to make easily available the basics of both the theory of hyperbolic conservation laws and the theory of systems of reaction-diffusion equations, including the generalized Morse theory as developed by C. Conley. These important subjects seem difficult to learn since the results are scattered throughout the research journals. 1 Second, I feel that there is a need to present the modern methods and ideas in these fields to a wider audience than just mathe maticians. Thus, the book has some rather sophisticated aspects to it, as well as certain textbook aspects. The latter serve to explain, somewhat, the reason that a book with the title Shock Waves and Reaction-Diffusion Equations has the first nine chapters devoted to linear partial differential equations. More precisely, I have found from my classroom experience that it is far easier to grasp the subtleties of nonlinear partial differential equations after one has an understanding of the basic notions in the linear theory. This book is divided into four main parts: linear theory, reaction diffusion equations, shock wave theory, and the Conley index, in that order. Thus, the text begins with a discussion of ill-posed problems.

Bifurcation Phenomena in Mathematical Physics and Related Topics

Author : C. Bardos
Publisher : Springer Science & Business Media
ISBN 13 : 9400990049
Total Pages : 591 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Bifurcation Phenomena in Mathematical Physics and Related Topics by : C. Bardos

Download or read book Bifurcation Phenomena in Mathematical Physics and Related Topics written by C. Bardos and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the main ideas in organizing the Summer Institute of Cargese on "Bifurcation Phenomena in Mathematical Physics and Related Topics" was to bring together Physicists and Mathematicians working on the properties arising from the non linearity of the phenomena and of the models that are used for their description. Among these properties the existence of bifurcations is one of the most interesting, and we had a general survey of the mathematical tools used in this field. This survey was done by M. Crandall and P. Rabinowitz and the notes enclosed in these proceedings were written by E. Buzano a]ld C. Canuto. Another mathematical approach, using Morse Theory was given by J. Smoller reporting on a joint work with C. Conley. An example of a direct application was given by M. Ghil. For physicists the theory of bifurcation is closely related to critical phenomena and this was explained in a series of talks given by J.P. Eckmann, G. Baker and M. Fisher. Some related ideas can be found in the talk given by T. T. Wu , on a joint work with Barry Mc Coy on quantum field theory. The description of these phenomena leads to the use of Pade approximants (it is explained for instance in the lectures of J. Nuttall) and then to some problems in drop hot moment problems. (cf. the lecture of D. Bessis).

The Structure of Attractors in Dynamical Systems

Author : N.G. Markley
Publisher : Springer
ISBN 13 : 3540357513
Total Pages : 275 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis The Structure of Attractors in Dynamical Systems by : N.G. Markley

Download or read book The Structure of Attractors in Dynamical Systems written by N.G. Markley and published by Springer. This book was released on 2007-01-05 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear and Adaptive Control

Author : Alan S.I. Zinober
Publisher : Springer
ISBN 13 : 3540458026
Total Pages : 396 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Nonlinear and Adaptive Control by : Alan S.I. Zinober

Download or read book Nonlinear and Adaptive Control written by Alan S.I. Zinober and published by Springer. This book was released on 2003-07-01 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of the EU Nonlinear Control Network Workshop was to bring together scientists who are already active in nonlinear control and young researchers working in this field. This book presents selectively invited contributions from the workshop, some describing state-of-the-art subjects that already have a status of maturity while others propose promising future directions in nonlinear control. Amongst others, following topics of nonlinear and adaptive control are included: adaptive and robust control, applications in physical systems, distributed parameter systems, disturbance attenuation, dynamic feedback, optimal control, sliding mode control, and tracking and motion planning.

Encyclopaedia of Mathematics

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 1556080085
Total Pages : 556 pages
Book Rating : 4.5/5 (56 download)

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Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel

Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 1993-01-31 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.