Semiflows On Topological Spaces
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Semiflows On Topological Spaces
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Author : Mauro Patrão
language : en
Publisher:
Release Date : 2005
Semiflows On Topological Spaces written by Mauro Patrão and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Flows (Differentiable dynamical systems) categories.
Morse Decomposition Of Semiflows On Topological Spaces
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Author : Mauro Patrão
language : en
Publisher:
Release Date : 2005
Morse Decomposition Of Semiflows On Topological Spaces written by Mauro Patrão and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Compact spaces categories.
Lyapunov Stability Of Transformation Semigroups
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Author : Victor H. L. Rocha
language : en
Publisher: Springer Nature
Release Date : 2025-04-10
Lyapunov Stability Of Transformation Semigroups written by Victor H. L. Rocha and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-10 with Mathematics categories.
This book presents recent research results on Lyapunov stability and attraction for semigroup actions in a pedagogical format, providing the reader with numerous modern ideas and mathematical formulations for dynamical concepts in the transformation group theory. In recent decades, many fundamental concepts of dynamical systems have been extended to the general framework of transformation semigroups. Limit sets, attractors, isolated invariant sets, prolongational limit sets, and stable sets now have semigroup theoretical analogues. This monograph consolidates recent advancements in this field in a way that makes it accessible to graduate students. An effort was made to relate the presented results to important recurrence notions, for contextual clarity. A rudimentary understanding of group theory and topology, including the concepts of semigroup action, orbit, fiber bundle, compactness, and connectedness, is a prerequisite for reading this text. As a valuable resource for research projects and academic dissertations on topological dynamics, geometry, and mathematical analysis, this work can potentially open new avenues for further research.
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.
The Dynamic Morse Theory Of Control Systems
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Author : Josiney Souza
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2020-01-20
The Dynamic Morse Theory Of Control Systems written by Josiney Souza and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-20 with Mathematics categories.
This book provides insights into the dynamics of control systems with the integration of conceptions such as stability, controllability, attraction, and chain transitivity. It highlights the importance of Morse theory with its feature of describing the global dynamics of systems, presented here for the first time in control theory. The mathematical formulations are comprehensive, designed especially for students, researches, and professionals interested in qualitative studies of control systems. The reader will find the book an accessible source of basic definitions, properties, methods, examples, theorems, references, lists of problems, and open questions. Parts of the book may be used for courses or seminars in mathematics or control-theoretic engineering, and its reference guide will serve as a great resource for research projects and academic dissertations on control theory or dynamical systems.
Attractors For Infinite Dimensional Non Autonomous Dynamical Systems
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Author : Alexandre Carvalho
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-25
Attractors For Infinite Dimensional Non Autonomous Dynamical Systems written by Alexandre Carvalho 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 2012-09-25 with Mathematics categories.
The book treats the theory of attractors for non-autonomous dynamical systems. The aim of the book is to give a coherent account of the current state of the theory, using the framework of processes to impose the minimum of restrictions on the nature of the non-autonomous dependence. The book is intended as an up-to-date summary of the field, but much of it will be accessible to beginning graduate students. Clear indications will be given as to which material is fundamental and which is more advanced, so that those new to the area can quickly obtain an overview, while those already involved can pursue the topics we cover more deeply.
Attractors Under Autonomous And Non Autonomous Perturbations
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Author : Matheus C. Bortolan
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-05-29
Attractors Under Autonomous And Non Autonomous Perturbations written by Matheus C. Bortolan 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 2020-05-29 with Education categories.
This book provides a comprehensive study of how attractors behave under perturbations for both autonomous and non-autonomous problems. Furthermore, the forward asymptotics of non-autonomous dynamical systems is presented here for the first time in a unified manner. When modelling real world phenomena imprecisions are unavoidable. On the other hand, it is paramount that mathematical models reflect the modelled phenomenon, in spite of unimportant neglectable influences discounted by simplifications, small errors introduced by empirical laws or measurements, among others. The authors deal with this issue by investigating the permanence of dynamical structures and continuity properties of the attractor. This is done in both the autonomous (time independent) and non-autonomous (time dependent) framework in four distinct levels of approximation: the upper semicontinuity, lower semicontinuity, topological structural stability and geometrical structural stability. This book is aimed at graduate students and researchers interested in dissipative dynamical systems and stability theory, and requires only a basic background in metric spaces, functional analysis and, for the applications, techniques of ordinary and partial differential equations.
Fractals And Hyperspaces
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Author : Keith R. Wicks
language : en
Publisher: Springer
Release Date : 2006-11-14
Fractals And Hyperspaces written by Keith R. Wicks 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.
Addressed to all readers with an interest in fractals, hyperspaces, fixed-point theory, tilings and nonstandard analysis, this book presents its subject in an original and accessible way complete with many figures. The first part of the book develops certain hyperspace theory concerning the Hausdorff metric and the Vietoris topology, as a foundation for what follows on self-similarity and fractality. A major feature is that nonstandard analysis is used to obtain new proofs of some known results much more slickly than before. The theory of J.E. Hutchinson's invariant sets (sets composed of smaller images of themselves) is developed, with a study of when such a set is tiled by its images and a classification of many invariant sets as either regular or residual. The last and most original part of the book introduces the notion of a "view" as part of a framework for studying the structure of sets within a given space. This leads to new, elegant concepts (defined purely topologically) of self-similarity and fractality: in particular, the author shows that many invariant sets are "visually fractal", i.e. have infinite detail in a certain sense. These ideas have considerable scope for further development, and a list of problems and lines of research is included.
Invariant Probabilities Of Transition Functions
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Author : Radu Zaharopol
language : en
Publisher: Springer
Release Date : 2014-06-27
Invariant Probabilities Of Transition Functions written by Radu Zaharopol and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-27 with Mathematics categories.
The structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transition functions, and are studied in this book. The results obtained are useful in ergodic theory and the theory of dynamical systems, which, in turn, can be applied in various other areas (like number theory). They are illustrated using transition functions defined by flows, semiflows, and one-parameter convolution semigroups of probability measures. In this book, all results on transition probabilities that have been published by the author between 2004 and 2008 are extended to transition functions. The proofs of the results obtained are new. For transition functions that satisfy very general conditions the book describes an ergodic decomposition that provides relevant information on the structure of the corresponding set of invariant probabilities. Ergodic decomposition means a splitting of the state space, where the invariant ergodic probability measures play a significant role. Other topics covered include: characterizations of the supports of various types of invariant probability measures and the use of these to obtain criteria for unique ergodicity, and the proofs of two mean ergodic theorems for a certain type of transition functions. The book will be of interest to mathematicians working in ergodic theory, dynamical systems, or the theory of Markov processes. Biologists, physicists and economists interested in interacting particle systems and rigorous mathematics will also find this book a valuable resource. Parts of it are suitable for advanced graduate courses. Prerequisites are basic notions and results on functional analysis, general topology, measure theory, the Bochner integral and some of its applications.
An Introduction To Semiflows
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Author : Albert J. Milani
language : en
Publisher: CRC Press
Release Date : 2004-10-14
An Introduction To Semiflows written by Albert J. Milani and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-14 with Mathematics categories.
This book introduces the class of dynamical systems called semiflows, which includes systems defined or modeled by certain types of differential evolution equations (DEEs). It focuses on the basic results of the theory of dynamical systems that can be extended naturally and applied to study the asymptotic behavior of the solutions of DEEs. The auth