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Author : Jonathan Martin Jacobs
Publisher : Unknown
Page : 352 pages
File Size : 50,5 Mb
Release : 1985
Category : Fixed point theory
ISBN : WISC:89010917128
Author : Nessim Sibony,Dierk Schleicher,Dinh Tien Cuong,Marco Brunella,Eric Bedford,Marco Abate
Publisher : Springer Science & Business Media
Page : 357 pages
File Size : 54,5 Mb
Release : 2010-07-31
Category : Mathematics
ISBN : 9783642131707
The theory of holomorphic dynamical systems is a subject of increasing interest in mathematics, both for its challenging problems and for its connections with other branches of pure and applied mathematics. A holomorphic dynamical system is the datum of a complex variety and a holomorphic object (such as a self-map or a vector ?eld) acting on it. The study of a holomorphic dynamical system consists in describing the asymptotic behavior of the system, associating it with some invariant objects (easy to compute) which describe the dynamics and classify the possible holomorphic dynamical systems supported by a given manifold. The behavior of a holomorphic dynamical system is pretty much related to the geometry of the ambient manifold (for instance, - perbolic manifolds do no admit chaotic behavior, while projective manifolds have a variety of different chaotic pictures). The techniques used to tackle such pr- lems are of variouskinds: complexanalysis, methodsof real analysis, pluripotential theory, algebraic geometry, differential geometry, topology. To cover all the possible points of view of the subject in a unique occasion has become almost impossible, and the CIME session in Cetraro on Holomorphic Dynamical Systems was not an exception.
Author : Martin Golubitsky,John Guckenheimer,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 408 pages
File Size : 49,9 Mb
Release : 1986
Category : Mathematics
ISBN : 9780821850602
This 1985 AMS Summer Research Conference brought together mathematicians interested in multiparameter bifurcation with scientists working on fluid instabilities and chemical reactor dynamics. This proceedings volume demonstrates the mutually beneficial interactions between the mathematical analysis, based on genericity, and experimental studies in these fields. Various papers study steady state bifurcation, Hopf bifurcation to periodic solutions, interactions between modes, dynamic bifurcations, and the role of symmetries in such systems. A section of abstracts at the end of the volume provides guides and pointers to the literature. The mathematical study of multiparameter bifurcation leads to a number of theoretical and practical difficulties, many of which are discussed in these papers. The articles also describe theoretical and experimental studies of chemical reactors, which provide many situations in which to test the mathematical ideas. Other test areas are found in fluid dynamics, particularly in studying the routes to chaos in two laboratory systems, Taylor-Couette flow between rotating cylinders and Rayleigh-Benard convection in a fluid layer.
Author : Santiago Ibáñez,Jesús S. Pérez del Río,Antonio Pumariño,J. Ángel Rodríguez
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 50,5 Mb
Release : 2013-09-20
Category : Mathematics
ISBN : 9783642388309
This book contains papers based on talks given at the International Conference Dynamical Systems: 100 years after Poincaré held at the University of Oviedo, Gijón in Spain, September 2012. It provides an overview of the state of the art in the study of dynamical systems. This book covers a broad range of topics, focusing on discrete and continuous dynamical systems, bifurcation theory, celestial mechanics, delay difference and differential equations, Hamiltonian systems and also the classic challenges in planar vector fields. It also details recent advances and new trends in the field, including applications to a wide range of disciplines such as biology, chemistry, physics and economics. The memory of Henri Poincaré, who laid the foundations of the subject, inspired this exploration of dynamical systems. In honor of this remarkable mathematician, theoretical physicist, engineer and philosopher, the authors have made a special effort to place the reader at the frontiers of current knowledge in the discipline.
Author : James D. Meiss
Publisher : SIAM
Page : 409 pages
File Size : 51,6 Mb
Release : 2007-01-01
Category : Mathematics
ISBN : 0898718236
Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems conceptsflow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems. Audience This textbook is intended for senior undergraduates and first-year graduate students in pure and applied mathematics, engineering, and the physical sciences. Readers should be comfortable with elementary differential equations and linear algebra and should have had exposure to advanced calculus. Contents List of Figures; Preface; Acknowledgments; Chapter 1: Introduction; Chapter 2: Linear Systems; Chapter 3: Existence and Uniqueness; Chapter 4: Dynamical Systems; Chapter 5: Invariant Manifolds; Chapter 6: The Phase Plane; Chapter 7: Chaotic Dynamics; Chapter 8: Bifurcation Theory; Chapter 9: Hamiltonian Dynamics; Appendix: Mathematical Software; Bibliography; Index
Author : J.K. Hale,L.T. Magalhaes,W.M. Oliva
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 55,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475744934
Including: An Introduction to the Homotopy Theory in Noncompact Spaces
Author : Tönu Puu
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 45,6 Mb
Release : 2013-03-19
Category : Mathematics
ISBN : 9783540246992
Attractors, Bifurcations, & Chaos - now in its second edition - begins with an introduction to mathematical methods in modern nonlinear dynamics and deals with differential equations. Phenomena such as bifurcations and deterministic chaos are given considerable emphasis, both in the methodological part, and in the second part, containing various applications in economics and in regional science. Coexistence of attractors and the multiplicity of development paths in nonlinear systems are central topics. The applications focus on issues such as business cycles, oligopoly, interregional trade dynamics, and economic development theory.
Author : Philip Holmes
Publisher : Cambridge University Press
Page : 403 pages
File Size : 49,5 Mb
Release : 2012-02-23
Category : Mathematics
ISBN : 9781107008250
Describes methods revealing the structures and dynamics of turbulence for engineering, physical science and mathematics researchers working in fluid dynamics.
Author : John Mallet-Paret,Jianhong Wu,Huaiping Zhu,Yingfie Yi
Publisher : Springer Science & Business Media
Page : 495 pages
File Size : 41,9 Mb
Release : 2012-10-11
Category : Mathematics
ISBN : 9781461445227
This collection covers a wide range of topics of infinite dimensional dynamical systems generated by parabolic partial differential equations, hyperbolic partial differential equations, solitary equations, lattice differential equations, delay differential equations, and stochastic differential equations. Infinite dimensional dynamical systems are generated by evolutionary equations describing the evolutions in time of systems whose status must be depicted in infinite dimensional phase spaces. Studying the long-term behaviors of such systems is important in our understanding of their spatiotemporal pattern formation and global continuation, and has been among major sources of motivation and applications of new developments of nonlinear analysis and other mathematical theories. Theories of the infinite dimensional dynamical systems have also found more and more important applications in physical, chemical, and life sciences. This book collects 19 papers from 48 invited lecturers to the International Conference on Infinite Dimensional Dynamical Systems held at York University, Toronto, in September of 2008. As the conference was dedicated to Professor George Sell from University of Minnesota on the occasion of his 70th birthday, this collection reflects the pioneering work and influence of Professor Sell in a few core areas of dynamical systems, including non-autonomous dynamical systems, skew-product flows, invariant manifolds theory, infinite dimensional dynamical systems, approximation dynamics, and fluid flows.
Author : G. C. Layek
Publisher : Springer Nature
Page : 701 pages
File Size : 49,7 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 9789819976959
Author : Conference Board of the Mathematical Sciences
Publisher : CRC Press
Page : 260 pages
File Size : 40,5 Mb
Release : 1981-09-01
Category : Mathematics
ISBN : 0824715292
Author : Bernold Fiedler
Publisher : Springer Science & Business Media
Page : 816 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642565892
Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.
Author : Ralph Abraham,Laura Gardini,Christian Mira
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 43,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781461219361
The materials in the book and on the accompanying disc are not solely developed with only the researcher and professional in mind, but also with consideration for the student: most of this material has been class-tested by the authors. The book is packed with some 100 computer graphics to illustrate the material, and the CD-ROM contains full-colour animations tied directly to the subject matter of the book itself. The cross-platform CD also contains the program ENDO, which enables users to create their own 2-D imagery with X-Windows. Maple scripts are provided to allow readers to work directly with the code from which the graphics in the book were taken.
Author : H.W. Broer,F. Dumortier,S.J. van Strien,F. Takens
Publisher : Elsevier
Page : 323 pages
File Size : 46,8 Mb
Release : 1991-11-05
Category : Science
ISBN : 9780444596253
The study of non-linear dynamical systems nowadays is an intricate mixture of analysis, geometry, algebra and measure theory and this book takes all aspects into account. Presenting the contents of its authors' graduate courses in non-linear dynamical systems, this volume aims at researchers who wish to be acquainted with the more theoretical and fundamental subjects in non-linear dynamics and is designed to link the popular literature with research papers and monographs. All of the subjects covered in this book are extensively dealt with and presented in a pedagogic form. These include the presentation of an environment for the route to chaos by quasi-periodicity (which is related to the Landau-Lifschitz and Ruelle-Takens scenario's concerning the onset of turbulence); the theories of 1-dimensional dynamics, singularities in planar vector fields, and quasi-periodicity in dissipative systems.
Author : Lui Lam
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 53,5 Mb
Release : 2003-11-14
Category : Science
ISBN : 038740614X
This textbook provides an introduction to the new science of nonlinear physics for advanced undergraduates, beginning graduate students, and researchers entering the field. The chapters, by pioneers and experts in the field, share a unified perspective. Nonlinear science developed out of the increasing ability to investigate and analyze systems for which effects are not simply linear functions of their causes; it is associated with such well-known code words as chaos, fractals, pattern formation, solitons, cellular automata, and complex systems. Nonlinear phenomena are important in many fields, including dynamical systems, fluid dynamics, materials science, statistical physics, and paritcel physics. The general principles developed in this text are applicable in a wide variety of fields in the natural and social sciences. The book will thus be of interest not only to physicists, but also to engineers, chemists, geologists, biologists, economists, and others interested in nonlinear phenomena. Examples and exercises complement the text, and extensive references provide a guide to research in the field.