Almost Automorphic And Almost Periodic Dynamics In Skew Product Semiflows
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Almost Automorphic And Almost Periodic Dynamics In Skew Product Semiflows
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Author : Wenxian Shen
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Almost Automorphic And Almost Periodic Dynamics In Skew Product Semiflows written by Wenxian Shen 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 1998 with Mathematics categories.
This volume is devoted to the study of almost automorphic dynamics in differential equations. By making use of techniques from abstract topological dynamics, it is shown that almost automorphy, a notion which was introduced by S. Bochner in 1955, is essential and fundamental in the qualitative study of almost periodic differential equations.
Stability And Bifurcation Theory For Non Autonomous Differential Equations
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Author : Anna Capietto
language : en
Publisher: Springer
Release Date : 2012-12-14
Stability And Bifurcation Theory For Non Autonomous Differential Equations written by Anna Capietto and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-14 with Mathematics categories.
This volume contains the notes from five lecture courses devoted to nonautonomous differential systems, in which appropriate topological and dynamical techniques were described and applied to a variety of problems. The courses took place during the C.I.M.E. Session "Stability and Bifurcation Problems for Non-Autonomous Differential Equations," held in Cetraro, Italy, June 19-25 2011. Anna Capietto and Jean Mawhin lectured on nonlinear boundary value problems; they applied the Maslov index and degree-theoretic methods in this context. Rafael Ortega discussed the theory of twist maps with nonperiodic phase and presented applications. Peter Kloeden and Sylvia Novo showed how dynamical methods can be used to study the stability/bifurcation properties of bounded solutions and of attracting sets for nonautonomous differential and functional-differential equations. The volume will be of interest to all researchers working in these and related fields.
Featured Reviews In Mathematical Reviews 1997 1999
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Author : Donald G. Babbitt
language : en
Publisher: American Mathematical Soc.
Release Date : 2000-05-05
Featured Reviews In Mathematical Reviews 1997 1999 written by Donald G. Babbitt 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 2000-05-05 with Mathematics categories.
This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.
Almost Periodic Type Functions And Ergodicity
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Author : Zhang Chuanyi
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-06-30
Almost Periodic Type Functions And Ergodicity written by Zhang Chuanyi 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 2003-06-30 with Mathematics categories.
The theory of almost periodic functions was first developed by the Danish mathematician H. Bohr during 1925-1926. Then Bohr's work was substantially extended by S. Bochner, H. Weyl, A. Besicovitch, J. Favard, J. von Neumann, V. V. Stepanov, N. N. Bogolyubov, and oth ers. Generalization of the classical theory of almost periodic functions has been taken in several directions. One direction is the broader study of functions of almost periodic type. Related this is the study of ergodic ity. It shows that the ergodicity plays an important part in the theories of function spectrum, semigroup of bounded linear operators, and dynamical systems. The purpose of this book is to develop a theory of almost pe riodic type functions and ergodicity with applications-in particular, to our interest-in the theory of differential equations, functional differen tial equations and abstract evolution equations. The author selects these topics because there have been many (excellent) books on almost periodic functions and relatively, few books on almost periodic type and ergodicity. The author also wishes to reflect new results in the book during recent years. The book consists of four chapters. In the first chapter, we present a basic theory of four almost periodic type functions. Section 1. 1 is about almost periodic functions. To make the reader easily learn the almost periodicity, we first discuss it in scalar case. After studying a classical theory for this case, we generalize it to finite dimensional vector-valued case, and finally, to Banach-valued (including Hilbert-valued) situation.
Dynamical Systems
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Author : S.-N. Chow
language : en
Publisher: Springer
Release Date : 2003-12-10
Dynamical Systems written by S.-N. Chow and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-10 with Mathematics categories.
The C.I.M.E. session on Dynamical Systems, held in Cetraro (Italy), June 19-26, 2000, focused on the latest developments in several important areas in dynamical systems, with full development and historical context. The lectures of Chow and Mallet-Paret focus on the area of lattice differential systems, the lectures of Conto and Galleotti treat the classical problem of classification of orbits for two-dimensional autonomous systems with polynomial right sides, the lectures of Nussbaum focus on applications of fixed point theorems to the problem of limiting profiles for the solutions of singular perturbations of delay differential equations, and the lectures of Johnson and Mantellini deal with the existence of periodic and quasi-periodic orbits to non-autonomous systems. The volume will be of interest to researchers and graduate students working in these areas.
Dynamical Systems In Population Biology
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Author : Xiao-Qiang Zhao
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-05
Dynamical Systems In Population Biology written by Xiao-Qiang Zhao 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 2013-06-05 with Mathematics categories.
Population dynamics is an important subject in mathematical biology. A cen tral problem is to study the long-term behavior of modeling systems. Most of these systems are governed by various evolutionary equations such as difference, ordinary, functional, and partial differential equations (see, e. g. , [165, 142, 218, 119, 55]). As we know, interactive populations often live in a fluctuating environment. For example, physical environmental conditions such as temperature and humidity and the availability of food, water, and other resources usually vary in time with seasonal or daily variations. Therefore, more realistic models should be nonautonomous systems. In particular, if the data in a model are periodic functions of time with commensurate period, a periodic system arises; if these periodic functions have different (minimal) periods, we get an almost periodic system. The existing reference books, from the dynamical systems point of view, mainly focus on autonomous biological systems. The book of Hess [106J is an excellent reference for periodic parabolic boundary value problems with applications to population dynamics. Since the publication of this book there have been extensive investigations on periodic, asymptotically periodic, almost periodic, and even general nonautonomous biological systems, which in turn have motivated further development of the theory of dynamical systems. In order to explain the dynamical systems approach to periodic population problems, let us consider, as an illustration, two species periodic competitive systems dUI dt = !I(t,Ul,U2), (0.
Almost Periodicity And Almost Automorphy
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Author : Abdallah Afoukal
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-03-03
Almost Periodicity And Almost Automorphy written by Abdallah Afoukal and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-03 with Mathematics categories.
When we study differential equations in Banach spaces whose coefficients are linear unbounded operators, we feel that we are working in ordinary differential equations; however, the fact that the operator coefficients are unbounded makes things quite different from what is known in the classical case. Examples or applications for such equations are naturally found in the theory of partial differential equations. More specifically, if we give importance to the time variable at the expense of the spatial variables, we obtain an “ordinary differential equation” with respect to the variable which was put in evidence. Thus, for example, the heat or the wave equation gives rise to ordinary differential equations of this kind. Adding boundary conditions can often be translated in terms of considering solutions in some convenient functional Banach space. The theory of semigroups of operators provides an elegant approach to study this kind of systems. Therefore, we can frequently guess or even prove theorems on differential equations in Banach spaces looking at a corresponding pattern in finite dimensional ordinary differential equations.
Theory Of Translation Closedness For Time Scales
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Author : Chao Wang
language : en
Publisher: Springer Nature
Release Date : 2020-05-05
Theory Of Translation Closedness For Time Scales written by Chao Wang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-05 with Mathematics categories.
This monograph establishes a theory of classification and translation closedness of time scales, a topic that was first studied by S. Hilger in 1988 to unify continuous and discrete analysis. The authors develop a theory of translation function on time scales that contains (piecewise) almost periodic functions, (piecewise) almost automorphic functions and their related generalization functions (e.g., pseudo almost periodic functions, weighted pseudo almost automorphic functions, and more). Against the background of dynamic equations, these function theories on time scales are applied to study the dynamical behavior of solutions for various types of dynamic equations on hybrid domains, including evolution equations, discontinuous equations and impulsive integro-differential equations. The theory presented allows many useful applications, such as in the Nicholson`s blowfiles model; the Lasota-Wazewska model; the Keynesian-Cross model; in those realistic dynamical models with a more complex hibrid domain, considered under different types of translation closedness of time scales; and in dynamic equations on mathematical models which cover neural networks. This book provides readers with the theoretical background necessary for accurate mathematical modeling in physics, chemical technology, population dynamics, biotechnology and economics, neural networks, and social sciences.
Dynamical Systems And Their Applications In Biology
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Author : Shigui Ruan
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Dynamical Systems And Their Applications In Biology written by Shigui Ruan 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 2003 with Mathematics categories.
This volume is based on the proceedings of the International Workshop on Dynamical Systems and their Applications in Biology held at the Canadian Coast Guard College on Cape Breton Island (Nova Scotia, Canada). It presents a broad picture of the current research surrounding applications of dynamical systems in biology, particularly in population biology. The book contains 19 papers and includes articles on the qualitative and/or numerical analysis of models involving ordinary, partial, functional, and stochastic differential equations. Applications include epidemiology, population dynamics, and physiology. The material is suitable for graduate students and research mathematicians interested in ordinary differential equations and their applications in biology. Also available by Ruan, Wolkowicz, and Wu is Differential Equations with Applications to Biology, Volume 21 in the AMS series Fields Institute Communications.
Metrical Almost Periodicity And Applications To Integro Differential Equations
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Author : Marko Kostić
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-06-06
Metrical Almost Periodicity And Applications To Integro Differential Equations written by Marko Kostić and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-06 with Mathematics categories.
The theory of almost periodic functions is a very active field of research for scholars. This research monograph analyzes various classes of multi-dimensional metrically almost periodic type functions with values in complex Banach spaces. We provide many applications of our theoretical results to the abstract Volterra integro-differential inclusions in Banach spaces.