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Author : J.K. Hale,L.T. Magalhaes,W.M. Oliva
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 54,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475744934
Including: An Introduction to the Homotopy Theory in Noncompact Spaces
Author : James C. Robinson
Publisher : Cambridge University Press
Page : 488 pages
File Size : 52,7 Mb
Release : 2001-04-23
Category : Mathematics
ISBN : 0521632048
This book treats the theory of global attractors, a recent development in the theory of partial differential equations, in a way that also includes much of the traditional elements of the subject. As such it gives a quick but directed introduction to some fundamental concepts, and by the end proceeds to current research problems. Since the subject is relatively new, this is the first book to attempt to treat these various topics in a unified and didactic way. It is intended to be suitable for first year graduate students.
Author : Jack K. Hale,Luis T. Magalhães,Waldyr M. Oliva,Krzysztof P. Rybakowski
Publisher : Springer Science & Business Media
Page : 195 pages
File Size : 55,8 Mb
Release : 1984
Category : Mathematics
ISBN : 0387909311
Author : John Mallet-Paret,Jianhong Wu,Huaiping Zhu,Yingfie Yi
Publisher : Springer Science & Business Media
Page : 495 pages
File Size : 53,8 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 : Roger Temam
Publisher : Springer Science & Business Media
Page : 670 pages
File Size : 42,6 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781461206453
In this book the author presents the dynamical systems in infinite dimension, especially those generated by dissipative partial differential equations. This book attempts a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics and in other areas of sciences and technology. This second edition has been updated and extended.
Author : John Mallet-Paret,Jianhong Wu,Yingfei Yi,Huaiping Zhu
Publisher : Springer Science & Business Media
Page : 496 pages
File Size : 45,5 Mb
Release : 2012-10-11
Category : Mathematics
ISBN : 9781461445234
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 : Christian Pötzsche
Publisher : Springer Science & Business Media
Page : 422 pages
File Size : 51,7 Mb
Release : 2010-09-17
Category : Mathematics
ISBN : 9783642142574
The goal of this book is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes).
Author : Hans J. Zwart
Publisher : Springer
Page : 161 pages
File Size : 50,6 Mb
Release : 2014-03-12
Category : Science
ISBN : 3662183234
The monograph is addressed to researchers in the field of geometric theory of infinite dimensional systems. The author uses basic concepts of the infinite dimensional system theory, approximate controllability, initial observability, which are covered in the second and third chapter. The book is self-contained with respect to the notions of the geometric theory, although sometimes the author refers to the references for the finite dimensional case.
Author : James Robinson,Paul Glendinning
Publisher : Springer Science & Business Media
Page : 236 pages
File Size : 49,7 Mb
Release : 2001-05-31
Category : Mathematics
ISBN : 0792369769
Proceedings of the NATO Advanced Study Institute, Cambridge, UK, 21 August-1 September 1995
Author : Ruth F. Curtain,Hans Zwart
Publisher : Springer Science & Business Media
Page : 714 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461242246
Infinite dimensional systems is now an established area of research. Given the recent trend in systems theory and in applications towards a synthesis of time- and frequency-domain methods, there is a need for an introductory text which treats both state-space and frequency-domain aspects in an integrated fashion. The authors' primary aim is to write an introductory textbook for a course on infinite dimensional linear systems. An important consideration by the authors is that their book should be accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Consequently, all the mathematical background is summarized in an extensive appendix. For the majority of students, this would be their only acquaintance with infinite dimensional systems.
Author : Boris Khesin,Robert Wendt
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 45,5 Mb
Release : 2008-09-28
Category : Mathematics
ISBN : 9783540772637
This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. The text includes many exercises and open questions.
Author : Alexander Schmeding
Publisher : Cambridge University Press
Page : 284 pages
File Size : 41,8 Mb
Release : 2022-12-22
Category : Mathematics
ISBN : 9781009089302
Introducing foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, this text is based on Bastiani calculus. It focuses on two main areas of infinite-dimensional geometry: infinite-dimensional Lie groups and weak Riemannian geometry, exploring their connections to manifolds of (smooth) mappings. Topics covered include diffeomorphism groups, loop groups and Riemannian metrics for shape analysis. Numerous examples highlight both surprising connections between finite- and infinite-dimensional geometry, and challenges occurring solely in infinite dimensions. The geometric techniques developed are then showcased in modern applications of geometry such as geometric hydrodynamics, higher geometry in the guise of Lie groupoids, and rough path theory. With plentiful exercises, some with solutions, and worked examples, this will be indispensable for graduate students and researchers working at the intersection of functional analysis, non-linear differential equations and differential geometry. This title is also available as Open Access on Cambridge Core.
Author : Kenneth Meyer,Glen Hall
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 40,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475740738
The theory of Hamiltonian systems is a vast subject which can be studied from many different viewpoints. This book develops the basic theory of Hamiltonian differential equations from a dynamical systems point of view. That is, the solutions of the differential equations are thought of as curves in a phase space and it is the geometry of these curves that is the important object of study. The analytic underpinnings of the subject are developed in detail. The last chapter on twist maps has a more geometric flavor. It was written by Glen R. Hall. The main example developed in the text is the classical N-body problem, i.e., the Hamiltonian system of differential equations which describe the motion of N point masses moving under the influence of their mutual gravitational attraction. Many of the general concepts are applied to this example. But this is not a book about the N-body problem for its own sake. The N-body problem is a subject in its own right which would require a sizable volume of its own. Very few of the special results which only apply to the N-body problem are given.
Author : Boling Guo,Liming Ling,Yansheng Ma,Hui Yang
Publisher : de Gruyter
Page : 0 pages
File Size : 47,8 Mb
Release : 2018
Category : Mathematics
ISBN : 3110586991
This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the fi rst volume is on the existence and properties for attractors and inertial manifolds. This volume highlights the use of modern analytical tools and methods such as the geometric measure method, center manifold theory in infinite dimensions, the Melnihov method, spectral analysis and so on for infinite-dimensional dynamical systems. The second volume includes the properties of global attractors, the calculation of discrete attractors, structures of small dissipative dynamical systems, and the existence and stability of solitary waves. Contents Discrete attractor and approximate calculation Some properties of global attractor Structures of small dissipative dynamical systems Existence and stability of solitary waves
Author : Jack K. Hale,Luis T. Magalhaes,Waldyr Oliva
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 52,9 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387228969
State-of-the-art in qualitative theory of functional differential equations; Most of the new material has never appeared in book form and some not even in papers; Second edition updated with new topics and results; Methods discussed will apply to other equations and applications