Conley Index Theory
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Conley Index Theory
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Author : Konstantin Michael Mischaikow
language : en
Publisher:
Release Date : 1999
Conley Index Theory written by Konstantin Michael Mischaikow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Differentiable dynamical systems categories.
Nonautonomous Conley Index
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Author : Axel Jänig
language : en
Publisher:
Release Date : 2016
Nonautonomous Conley Index written by Axel Jänig and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
Conley index theory associates isolated invariant sets with an index e.g, a topological space. This theory is generalized to nonautonomous dynamical systems. A corresponding theory of Morse-decompositions is developed. Applications to dynamical systems obtained from ordinary and partial differential equations are discussed.eng
Rigorous Numerics Using Conley Index Theory
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Author : Ulrich Miller
language : en
Publisher:
Release Date : 2005
Rigorous Numerics Using Conley Index Theory written by Ulrich Miller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Exploring Global Dynamics
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Author : Michael Eidenschink
language : en
Publisher:
Release Date : 1996
Exploring Global Dynamics written by Michael Eidenschink and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Differentiable dynamical systems categories.
Isolated Invariant Sets And The Morse Index
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Author : Charles C. Conley
language : en
Publisher: American Mathematical Soc.
Release Date : 1978-12-31
Isolated Invariant Sets And The Morse Index written by Charles C. Conley and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978-12-31 with Mathematics categories.
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.
The Homotopy Index And Partial Differential Equations
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Author : Krzysztof P. Rybakowski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Homotopy Index And Partial Differential Equations written by Krzysztof P. Rybakowski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Handbook Of Dynamical Systems
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Author : B. Fiedler
language : en
Publisher: Gulf Professional Publishing
Release Date : 2002-02-21
Handbook Of Dynamical Systems written by B. Fiedler and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-02-21 with Science categories.
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.
Dynamical Systems
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Author : Ludwig Arnold
language : en
Publisher: Springer
Release Date : 2006-11-14
Dynamical Systems written by Ludwig Arnold and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
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.
Topological Methods Variational Methods And Their Applications
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Author : Haim Brzis
language : en
Publisher: World Scientific
Release Date : 2003
Topological Methods Variational Methods And Their Applications written by Haim Brzis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
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.
Topological Methods Variational Methods And Their Applications
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Author : H Brezis
language : en
Publisher: World Scientific
Release Date : 2003-03-13
Topological Methods Variational Methods And Their Applications written by H Brezis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-13 with Mathematics categories.
ICM 2002 Satellite Conference on Nonlinear Analysis was held in the period: August 14–18, 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 Schrödinger equations, semilinear elliptic equations, Hamiltonian systems, central configuration in N-body problems and variational problems arising in geometry and physics. Contents:The Underlying Geometry of the Fixed Centers Problems (A Albouy)Critical Equations for the Polyharmonic Operator (T Bartsch)Heat Method in Nonlinear Elliptic Equations (K-C Chang)Boundary Blow-Up Solutions and Their Applications (Y H Du)Fixed Points of Increasing Operator (F Y Li)Collinear Central Configurations in Celestial Mechanics (Y M Long & S Z Sun)Remarks on a Priori Estimates for Superlinear Elliptic Problems (M Ramos)A Semilinear Schrödinger Equation with Magnetic Field (A Szulkin)Sign Changing Solutions of Superlinear Schrödinger Equations (T Weth)Computational Theory and Methods for Finding Multiple Critical Points (J X Zhou)and other papers Readership: Researchers and graduate students in nonlinear differential equations, nonlinear functional analysis, dynamical systems, mathematical physics etc. Keywords:Variational Mthods;Topological Methods;Hamiltonian Systems;Nonlinear Schrödinger Equation;Dynamic System