Homotopy Methods In Topological Fixed And Periodic Points Theory

Author : Jerzy Jezierski,Waclaw Marzantowicz
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 43,7 Mb
Release : 2006-01-17
Category : Mathematics
ISBN : 9781402039317

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Homotopy Methods in Topological Fixed and Periodic Points Theory by Jerzy Jezierski,Waclaw Marzantowicz Pdf

The notion of a ?xed point plays a crucial role in numerous branches of mat- maticsand its applications. Informationabout the existence of such pointsis often the crucial argument in solving a problem. In particular, topological methods of ?xed point theory have been an increasing focus of interest over the last century. These topological methods of ?xed point theory are divided, roughly speaking, into two types. The ?rst type includes such as the Banach Contraction Principle where the assumptions on the space can be very mild but a small change of the map can remove the ?xed point. The second type, on the other hand, such as the Brouwer and Lefschetz Fixed Point Theorems, give the existence of a ?xed point not only for a given map but also for any its deformations. This book is an exposition of a part of the topological ?xed and periodic point theory, of this second type, based on the notions of Lefschetz and Nielsen numbers. Since both notions are homotopyinvariants, the deformationis used as an essential method, and the assertions of theorems typically state the existence of ?xed or periodic points for every map of the whole homotopy class, we refer to them as homotopy methods of the topological ?xed and periodic point theory.

Author : Robert F. Brown
Publisher : Springer Science & Business Media
Page : 990 pages
File Size : 50,8 Mb
Release : 2005-07-21
Category : Mathematics
ISBN : 1402032218

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Handbook of Topological Fixed Point Theory by Robert F. Brown Pdf

This book will be especially useful for post-graduate students and researchers interested in the fixed point theory, particularly in topological methods in nonlinear analysis, differential equations and dynamical systems. The content is also likely to stimulate the interest of mathematical economists, population dynamics experts as well as theoretical physicists exploring the topological dynamics.

Author : Lech Górniewicz
Publisher : Springer Science & Business Media
Page : 548 pages
File Size : 51,7 Mb
Release : 2006-06-03
Category : Mathematics
ISBN : 9781402046667

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Topological Fixed Point Theory of Multivalued Mappings by Lech Górniewicz Pdf

This book is devoted to the topological fixed point theory of multivalued mappings including applications to differential inclusions and mathematical economy. It is the first monograph dealing with the fixed point theory of multivalued mappings in metric ANR spaces. Although the theoretical material was tendentiously selected with respect to applications, the text is self-contained. Current results are presented.

Author : Boju Jiang
Publisher : Springer
Page : 209 pages
File Size : 55,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540468622

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Topological Fixed Point Theory and Applications by Boju Jiang Pdf

This selection of papers from the Beijing conference gives a cross-section of the current trends in the field of fixed point theory as seen by topologists and analysts. Apart from one survey article, they are all original research articles, on topics including equivariant theory, extensions of Nielsen theory, periodic orbits of discrete and continuous dynamical systems, and new invariants and techniques in topological approaches to analytic problems.

Author : Rafael Ortega
Publisher : Walter de Gruyter GmbH & Co KG
Page : 195 pages
File Size : 55,5 Mb
Release : 2019-05-06
Category : Mathematics
ISBN : 9783110551167

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Periodic Differential Equations in the Plane by Rafael Ortega Pdf

Periodic differential equations appear in many contexts such as in the theory of nonlinear oscillators, in celestial mechanics, or in population dynamics with seasonal effects. The most traditional approach to study these equations is based on the introduction of small parameters, but the search of nonlocal results leads to the application of several topological tools. Examples are fixed point theorems, degree theory, or bifurcation theory. These well-known methods are valid for equations of arbitrary dimension and they are mainly employed to prove the existence of periodic solutions. Following the approach initiated by Massera, this book presents some more delicate techniques whose validity is restricted to two dimensions. These typically produce additional dynamical information such as the instability of periodic solutions, the convergence of all solutions to periodic solutions, or connections between the number of harmonic and subharmonic solutions. The qualitative study of periodic planar equations leads naturally to a class of discrete dynamical systems generated by homeomorphisms or embeddings of the plane. To study these maps, Brouwer introduced the notion of a translation arc, somehow mimicking the notion of an orbit in continuous dynamical systems. The study of the properties of these translation arcs is full of intuition and often leads to "non-rigorous proofs". In the book, complete proofs following ideas developed by Brown are presented and the final conclusion is the Arc Translation Lemma, a counterpart of the Poincaré–Bendixson theorem for discrete dynamical systems. Applications to differential equations and discussions on the topology of the plane are the two themes that alternate throughout the five chapters of the book.

Author : Marko Kostić
Publisher : Walter de Gruyter GmbH & Co KG
Page : 576 pages
File Size : 52,7 Mb
Release : 2023-06-06
Category : Mathematics
ISBN : 9783111233871

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Metrical Almost Periodicity and Applications to Integro-Differential Equations by Marko Kostić Pdf

Author : Sergiǐ Kolyada:,Martin Möller,Pieter Moree,Thomas Ward
Publisher : American Mathematical Soc.
Page : 315 pages
File Size : 43,8 Mb
Release : 2016-07-27
Category : Ergodic theory
ISBN : 9781470420208

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Dynamics and Numbers by Sergiǐ Kolyada:,Martin Möller,Pieter Moree,Thomas Ward Pdf

This volume contains a collection of survey and research articles from the special program and international conference on Dynamics and Numbers held at the Max-Planck Institute for Mathematics in Bonn, Germany in 2014. The papers reflect the great diversity and depth of the interaction between number theory and dynamical systems and geometry in particular. Topics covered in this volume include symbolic dynamics, Bratelli diagrams, geometry of laminations, entropy, Nielsen theory, recurrence, topology of the moduli space of interval maps, and specification properties.

Author : Valeri Obukhovskii,Pietro Zecca,Nguyen Van Loi,Sergei Kornev
Publisher : Springer
Page : 189 pages
File Size : 54,5 Mb
Release : 2013-05-13
Category : Mathematics
ISBN : 9783642370700

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Method of Guiding Functions in Problems of Nonlinear Analysis by Valeri Obukhovskii,Pietro Zecca,Nguyen Van Loi,Sergei Kornev Pdf

This book offers a self-contained introduction to the theory of guiding functions methods, which can be used to study the existence of periodic solutions and their bifurcations in ordinary differential equations, differential inclusions and in control theory. It starts with the basic concepts of nonlinear and multivalued analysis, describes the classical aspects of the method of guiding functions, and then presents recent findings only available in the research literature. It describes essential applications in control theory, the theory of bifurcations, and physics, making it a valuable resource not only for “pure” mathematicians, but also for students and researchers working in applied mathematics, the engineering sciences and physics.

Author : Jane Cronin
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 43,5 Mb
Release : 1995-01-05
Category : Fixed point theory
ISBN : 9780821815113

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Fixed points and topological degree in nonlinear analysis by Jane Cronin Pdf

The topological methods based on fixed-point theory and on local topological degree which have been developed by Leray, Schauder, Nirenberg, Cesari and others for the study of nonlinear differential equations are here described in detail, beginning with elementary considerations. The reader is not assumed to have any knowledge of topology beyond the theory of point sets in Euclidean n-space which ordinarily forms part of a course in advanced calculus. The methods are first developed for Euclidean n-space and applied to the study of existence and stability of periodic and almost-periodic solutions of systems of ordinary differential equations, both quasi-linear and with ``large'' nonlinearities. Then, after being extended to infinite-dimensional ``function-spaces'', these methods are applied to integral equations, partial differential equations and further problems concerning periodic solutions of ordinary differential equations.

Author : Hanno Ulrich
Publisher : Lecture Notes in Mathematics
Page : 168 pages
File Size : 55,7 Mb
Release : 1988-09-14
Category : Mathematics
ISBN : UOM:39015049299244

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Fixed Point Theory of Parametrized Equivariant Maps by Hanno Ulrich Pdf

The first part of this research monograph discusses general properties of G-ENRBs - Euclidean Neighbourhood Retracts over B with action of a compact Lie group G - and their relations with fibrations, continuous submersions, and fibre bundles. It thus addresses equivariant point set topology as well as equivariant homotopy theory. Notable tools are vertical Jaworowski criterion and an equivariant transversality theorem. The second part presents equivariant cohomology theory showing that equivariant fixed point theory is isomorphic to equivariant stable cohomotopy theory. A crucial result is the sum decomposition of the equivariant fixed point index which provides an insight into the structure of the theory's coefficient group. Among the consequences of the sum formula are some Borsuk-Ulam theorems as well as some folklore results on compact Lie-groups. The final section investigates the fixed point index in equivariant K-theory. The book is intended to be a thorough and comprehensive presentation of its subject. The reader should be familiar with the basics of the theory of compact transformation groups. Good knowledge of algebraic topology - both homotopy and homology theory - is assumed. For the advanced reader, the book may serve as a base for further research. The student will be introduced into equivariant fixed point theory; he may find it helpful for further orientation.

Author : John R. Graef,Johnny Henderson,Abdelghani Ouahab
Publisher : CRC Press
Page : 430 pages
File Size : 44,5 Mb
Release : 2018-09-25
Category : Mathematics
ISBN : 9780429822612

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Topological Methods for Differential Equations and Inclusions by John R. Graef,Johnny Henderson,Abdelghani Ouahab Pdf

Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. Since the dynamics of economic, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis.

Author : Anonim
Publisher : Unknown
Page : 684 pages
File Size : 40,6 Mb
Release : 2008
Category : Differentiable dynamical systems
ISBN : UOM:39015072621546

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Discrete and Continuous Dynamical Systems by Anonim Pdf

Author : Marcy Barge,Ams Special Session on Topology in Dynamics,Krystyna Kuperberg
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 50,9 Mb
Release : 1999
Category : Differentiable dynamical systems
ISBN : 9780821819586

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Geometry and Topology in Dynamics by Marcy Barge,Ams Special Session on Topology in Dynamics,Krystyna Kuperberg Pdf

This volume consists of the written presentations of lectures given at two special sessions: the AMS Special Session on Topology in Dynamics (Winston-Salem, NC) and the AMS-AWM Special Session on Geometry in Dynamics (San Antonio, TX). Each article concerns aspects of the topology or geometry of dynamical systems. Topics covered include the following: foliations and laminations, iterated function systems, the three-body problem, isotopy stability, homoclinic tangles, fractal dimension, Morse homology, knotted orbits, inverse limits, contact structures, Grassmanians, blowups, and continua. New results are presented reflecting current trends in topological aspects of dynamical systems. The book offers a wide variety of topics of special interest to those working this area bridging topology and dynamical systems.

Author : Zehan Jiang,Tse-han Chiang
Publisher : Springer Verlag
Page : 0 pages
File Size : 50,8 Mb
Release : 1989
Category : Mathematics
ISBN : 038710819X

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The Theory of Fixed Point Classes by Zehan Jiang,Tse-han Chiang Pdf

The General problem. A Particular Case. A Few historical Remarks.; The Nielsen Number;Evaluation of the Nielsen Number;Nielsen Number and the Least Number of Fixed Points;The Number N(f, H)and the RootCla;Homotopy and fundamental Group;Covering Spaces;Approximation Theorems.

Author : Michal Fečkan
Publisher : Springer Science & Business Media
Page : 266 pages
File Size : 48,6 Mb
Release : 2008-06-29
Category : Mathematics
ISBN : 9781402087240

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Topological Degree Approach to Bifurcation Problems by Michal Fečkan Pdf

1. 1 Preface Many phenomena from physics, biology, chemistry and economics are modeled by di?erential equations with parameters. When a nonlinear equation is est- lished, its behavior/dynamics should be understood. In general, it is impossible to ?nd a complete dynamics of a nonlinear di?erential equation. Hence at least, either periodic or irregular/chaotic solutions are tried to be shown. So a pr- erty of a desired solution of a nonlinear equation is given as a parameterized boundary value problem. Consequently, the task is transformed to a solvability of an abstract nonlinear equation with parameters on a certain functional space. When a family of solutions of the abstract equation is known for some para- ters, the persistence or bifurcations of solutions from that family is studied as parameters are changing. There are several approaches to handle such nonl- ear bifurcation problems. One of them is a topological degree method, which is rather powerful in cases when nonlinearities are not enough smooth. The aim of this book is to present several original bifurcation results achieved by the author using the topological degree theory. The scope of the results is rather broad from showing periodic and chaotic behavior of non-smooth mechanical systems through the existence of traveling waves for ordinary di?erential eq- tions on in?nite lattices up to study periodic oscillations of undamped abstract waveequationsonHilbertspaceswithapplicationstononlinearbeamandstring partial di?erential equations. 1.