Dichotomies in Stability Theory PDF Download
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Author: W. A. Coppel
Publisher: Springer
ISBN: 3540359761
Category : Mathematics
Languages : en
Pages : 103
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Book Description
Author: W. A. Coppel
Publisher: Springer
ISBN: 3540359761
Category : Mathematics
Languages : en
Pages : 103
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Book Description
Author: Yu. A. Mitropolsky
Publisher: CRC Press
ISBN: 9780415272216
Category : Mathematics
Languages : en
Pages : 394
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Book Description
Linear nonautonomous equations arise as mathematical models in mechanics, chemistry, and biology. The investigation of bounded solutions to systems of differential equations involves some important and challenging problems of perturbation theory for invariant toroidal manifolds. This monograph is a detailed study of the application of Lyapunov functions with variable sign, expressed in quadratic forms, to the solution of this problem. The authors explore the preservation of invariant tori of dynamic systems under perturbation. This volume is a classic contribution to the literature on stability theory and provides a useful source of reference for postgraduates and researchers.
Author: Yu. A. Mitropolsky
Publisher: CRC Press
ISBN: 1482264897
Category : Mathematics
Languages : en
Pages : 400
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Book Description
Linear nonautonomous equations arise as mathematical models in mechanics, chemistry, and biology. The investigation of bounded solutions to systems of differential equations involves some important and challenging problems of perturbation theory for invariant toroidal manifolds. This monograph is a detailed study of the application of Lyapunov func
Author: Horst Leipholz
Publisher: Springer-Verlag
ISBN: 3663106489
Category : Technology & Engineering
Languages : de
Pages : 359
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Book Description
Author: Everaldo M. Bonotto
Publisher: John Wiley & Sons
ISBN: 1119654939
Category : Mathematics
Languages : en
Pages : 514
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Book Description
GENERALIZED ORDINARY DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES AND APPLICATIONS Explore a unified view of differential equations through the use of the generalized ODE from leading academics in mathematics Generalized Ordinary Differential Equations in Abstract Spaces and Applications delivers a comprehensive treatment of new results of the theory of Generalized ODEs in abstract spaces. The book covers applications to other types of differential equations, including Measure Functional Differential Equations (measure FDEs). It presents a uniform collection of qualitative results of Generalized ODEs and offers readers an introduction to several theories, including ordinary differential equations, impulsive differential equations, functional differential equations, dynamical equations on time scales, and more. Throughout the book, the focus is on qualitative theory and on corresponding results for other types of differential equations, as well as the connection between Generalized Ordinary Differential Equations and impulsive differential equations, functional differential equations, measure differential equations and dynamic equations on time scales. The book’s descriptions will be of use in many mathematical contexts, as well as in the social and natural sciences. Readers will also benefit from the inclusion of: A thorough introduction to regulated functions, including their basic properties, equiregulated sets, uniform convergence, and relatively compact sets An exploration of the Kurzweil integral, including its definitions and basic properties A discussion of measure functional differential equations, including impulsive measure FDEs The interrelationship between generalized ODEs and measure FDEs A treatment of the basic properties of generalized ODEs, including the existence and uniqueness of solutions, and prolongation and maximal solutions Perfect for researchers and graduate students in Differential Equations and Dynamical Systems, Generalized Ordinary Differential Equations in Abstract Spaces and Applications will also earn a place in the libraries of advanced undergraduate students taking courses in the subject and hoping to move onto graduate studies.
Author: Jacques Leopold Willems
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 228
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Book Description
Author: Luis Barreira
Publisher: Springer
ISBN: 3540747753
Category : Mathematics
Languages : en
Pages : 288
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Book Description
This volume covers the stability of nonautonomous differential equations in Banach spaces in the presence of nonuniform hyperbolicity. Topics under discussion include the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, and the construction and regularity of topological conjugacies. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.
Author: Yu A. Mitropolskii
Publisher:
ISBN: 9789056992170
Category :
Languages : en
Pages :
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Book Description
Author: Zhensheng Lin
Publisher: World Scientific
ISBN: 9789810242831
Category : Mathematics
Languages : en
Pages : 222
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Book Description
Historically, the theory of stability is based on linear differential systems, which are simple and important systems in ordinary differential equations. The research on differential equations and on the theory of stability will, to a certain extent, be influenced by the research on linear differential systems. For differential linear equation systems, there are still many historical open questions attracting mathematicians. This book deals with the theory of linear differential systems developed around the notion of exponential dichotomies. The authors advance the theory of stability through their research in this field. Several new important results on linear differential systems are presented. They concern exponential dichotomy and the structure of the sets of hyperbolic points. The book has five chapters: Chapter 1 introduces some necessary classical results on the linear differential systems, and the following chapters discuss exponential dichotomy, spectra of almost periodic linear systems, the Floquet theory for quasi periodic linear systems and the structure of sets of hyperbolic points. This book is a very useful reference in the area of the stability theory of ordinary differential equations and the theory of dynamic systems.
Author: Horst H. E. Leipholz
Publisher: New York : Academic Press
ISBN:
Category : Science
Languages : en
Pages : 296
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Book Description
