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Linear Systems Exponential Dichotomy And Structure Of Sets Of Hyperbolic Points
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Book Synopsis Linear Systems And Exponential Dichotomy And Structure Of Sets Of Hyperbolic Points by : Zhensheng Lin
Download or read book Linear Systems And Exponential Dichotomy And Structure Of Sets Of Hyperbolic Points written by Zhensheng Lin and published by World Scientific. This book was released on 2000-04-28 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 first author advanced the theory of stability through his 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.
Book Synopsis Linear Systems Exponential Dichotomy and Structure of Sets of Hyperbolic Points by : Zhensheng Lin
Download or read book Linear Systems Exponential Dichotomy and Structure of Sets of Hyperbolic Points written by Zhensheng Lin and published by World Scientific. This book was released on 2000 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Generalized Ordinary Differential Equations in Abstract Spaces and Applications by : Everaldo M. Bonotto
Download or read book Generalized Ordinary Differential Equations in Abstract Spaces and Applications written by Everaldo M. Bonotto and published by John Wiley & Sons. This book was released on 2021-09-15 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Hamiltonian Dynamical Systems and the N-Body Problem by : Kenneth Meyer
Download or read book Introduction to Hamiltonian Dynamical Systems and the N-Body Problem written by Kenneth Meyer and published by Springer Science & Business Media. This book was released on 2008-12-05 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arising from a graduate course taught to math and engineering students, this text provides a systematic grounding in the theory of Hamiltonian systems, as well as introducing the theory of integrals and reduction. A number of other topics are covered too.
Download or read book Bibliographic Index written by and published by . This book was released on 2002 with total page 1080 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 872 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Well-posedness of Linear Hyperbolic Problems by : Aleksandr Mikhaĭlovich Blokhin
Download or read book Well-posedness of Linear Hyperbolic Problems written by Aleksandr Mikhaĭlovich Blokhin and published by Nova Publishers. This book was released on 2006 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book will be useful for students and specialists of partial differential equations and the mathematical sciences because it clarifies crucial points of Kreiss' symmetrizer technique. The Kreiss technique was developed by H.O. Kreiss for initial boundary value problems for linear hyperbolic systems. This technique is important because it involves equations that are used in many of the applied sciences. The research presented in this book takes unique approaches to exploring the Kreiss technique that will add insight and new perspectives to linear hyperbolic problems"--Publ. web site.
Book Synopsis Evolution Semigroups in Dynamical Systems and Differential Equations by : Carmen Chicone
Download or read book Evolution Semigroups in Dynamical Systems and Differential Equations written by Carmen Chicone and published by American Mathematical Soc.. This book was released on 1999 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of the book is the spectral theory for evolution operators and evolution semigroups, a subject tracing its origins to the classical results of J. Mather on hyperbolic dynamical systems and J. Howland on nonautonomous Cauchy problems. The authors use a wide range of methods and offer a unique presentation. The authors give a unifying approach for a study of infinite-dimensional nonautonomous problems, which is based on the consistent use of evolution semigroups. This unifying idea connects various questions in stability of semigroups, infinite-dimensional hyperbolic linear skew-product flows, translation Banach algebras, transfer operators, stability radii in control theory, Lyapunov exponents, magneto-dynamics and hydro-dynamics. Thus the book is much broader in scope than existing books on asymptotic behavior of semigroups. Included is a solid collection of examples from different areas of analysis, PDEs, and dynamical systems. This is the first monograph where the spectral theory of infinite dimensional linear skew-product flows is described together with its connection to the multiplicative ergodic theorem; the same technique is used to study evolution semigroups, kinematic dynamos, and Ruelle operators; the theory of stability radii, an important concept in control theory, is also presented. Examples are included and non-traditional applications are provided.
Book Synopsis Applied and Computational Measurable Dynamics by : Erik M. Bollt
Download or read book Applied and Computational Measurable Dynamics written by Erik M. Bollt and published by SIAM. This book was released on 2013-12-03 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Until recently, measurable dynamics has been held as a highly theoretical mathematical topic with few generally known obvious links for practitioners in areas of applied mathematics. However, the advent of high-speed computers, rapidly developing algorithms, and new numerical methods has allowed for a tremendous amount of progress and sophistication in efforts to represent the notion of a transfer operator discretely but to high resolution. This book connects many concepts in dynamical systems with mathematical tools from areas such as graph theory and ergodic theory. The authors introduce practical tools for applications related to measurable dynamical systems, coherent structures, and transport problems. The new and fast-developing computational tools discussed throughout the book allow for detailed analysis of real-world problems that are simply beyond the reach of traditional methods.
Book Synopsis Dynamics of Evolutionary Equations by : George R. Sell
Download or read book Dynamics of Evolutionary Equations written by George R. Sell and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory and applications of infinite dimensional dynamical systems have attracted the attention of scientists for quite some time. This book serves as an entrée for scholars beginning their journey into the world of dynamical systems, especially infinite dimensional spaces. The main approach involves the theory of evolutionary equations.
Book Synopsis Non-Linear Hyperbolic Equations in Domains with Conical Points by : Ingo Witt
Download or read book Non-Linear Hyperbolic Equations in Domains with Conical Points written by Ingo Witt and published by Wiley-VCH. This book was released on 1995-08-11 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes build to a proof of a local-in-time existence result for quasilinear hyperbolic evolution equations of second order in domains with conical points. In the first part, the existence of solutions to the corresponding linear equations is addressed, including the asymptotics of solutions near conical points. Using this information, the quasilinear equations are then solved by the standard iteration procedure. The exposition is based on Kato's semigroup-theoretic approach for solving abstract linear hyperbolic equations and Schulze's theory of pseudo-differential operators on manifolds with conical singularities. The former method provides the general framework, whereas the latter is the basic tool in treating the specific difficulties of the nonsmooth situation. Significantly, Schulze's theory admits a parameter-dependent version, which allows the description of the branching behaviour in time of discrete asymptotics of solutions near conical points. The calculus is presented in a form in which the operators are permitted to have symbols with limited smoothness, as arises in nonlinear problems. In an appendix, the applicability of energy methods is briefly discussed.
Book Synopsis Hyperbolic Structure of Time Discretizations and the Dependence on the Time Step by : Aaron Hagen
Download or read book Hyperbolic Structure of Time Discretizations and the Dependence on the Time Step written by Aaron Hagen and published by . This book was released on 1996 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Annals of Differential Equations by :
Download or read book Annals of Differential Equations written by and published by . This book was released on 1994 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Structure of the Set of Hyperbolic Systems of Partial Differential Equations by : Dale Marie Clarke
Download or read book The Structure of the Set of Hyperbolic Systems of Partial Differential Equations written by Dale Marie Clarke and published by . This book was released on 1981 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Volterra Equations by : S.-O. Londen
Download or read book Volterra Equations written by S.-O. Londen and published by Springer. This book was released on 2006-11-15 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions by numerous experts
Book Synopsis Exponential Dichotomy and Smooth Invariant Center Manifolds for Semilinear Hyperbolic Systems by : Mark Lichtner
Download or read book Exponential Dichotomy and Smooth Invariant Center Manifolds for Semilinear Hyperbolic Systems written by Mark Lichtner and published by . This book was released on 2006 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Global Attractors of Non-autonomous Dissipative Dynamical Systems by : David N. Cheban
Download or read book Global Attractors of Non-autonomous Dissipative Dynamical Systems written by David N. Cheban and published by World Scientific. This book was released on 2004 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of attractors of dynamical systems occupies an important position in the modern qualitative theory of differential equations. This engaging volume presents an authoritative overview of both autonomous and non-autonomous dynamical systems, including the global compact attractor.
