Описание: The nature of time in a nonautonomous dynamical system is very different from that in autonomous systems, which depend only on the time that has elapsed since starting rather than on the actual time itself.
This unique book's subject is meanders (connected, oriented, non-self-intersecting planar curves intersecting the horizontal line transversely) in the context of dynamical systems. By interpreting the transverse intersection points as vertices and the arches arising from these curves as directed edges, meanders are introduced from the graphtheoretical perspective. Supplementing the rigorous results, mathematical methods, constructions, and examples of meanders with a large number of insightful figures, issues such as connectivity and the number of connected components of meanders are studied in detail with the aid of collapse and multiple collapse, forks, and chambers. Moreover, the author introduces a large class of Morse meanders by utilizing the right and left one-shift maps, and presents connections to Sturm global attractors, seaweed and Frobenius Lie algebras, and the classical Yang-Baxter equation.
Описание: The study of attractors of dynamical systems occupies an important position in the modern qualitative theory of differential equations.
Автор: Xiaoying Han; Peter Kloeden Название: Attractors Under Discretisation ISBN: 3319619330 ISBN-13(EAN): 9783319619330 Издательство: Springer Рейтинг: Цена: 7685.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Part I Dynamical systems and numerical schemes.- 1 Lyapunov stability and dynamical systems.- 2 One step numerical schemes.- Part II Steady states under discretization.- 3 Linear systems.- 4 Lyapunov functions.- 5 Dissipative systems with steady states.- 6 Saddle points under discretisation . Part III Autonomous attractors under discretization.- 7 Dissipative systems with attractors.- 8 Lyapunov functions for attractors.- 9 Discretisation of an attractor. Part IV Nonautonomous limit sets under discretization.- 10 Dissipative nonautonomous systems .- 11 Discretisation of nonautonomous limit sets.- 12 Variable step size.- 13 Discretisation of a uniform pullback attractor.- Notes.- References.
Автор: Guo Boling, Ling Liming, Ma Yansheng Название: Attractors and Inertial Manifolds ISBN: 3110549255 ISBN-13(EAN): 9783110549256 Издательство: Walter de Gruyter Цена: 40403.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
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 first volume is on the mathematical analysis of attractors and inertial manifolds. This volume deals with the existence of global attractors, inertial manifolds and with the estimation of Hausdorff fractal dimension for some dissipative nonlinear evolution equations in modern physics. Known as well as many new results about the existence, regularity and properties of inertial manifolds and approximate inertial manifolds are also presented in the first volume. The second volume will be devoted to modern analytical tools and methods in infinite-dimensional dynamical systems.
Contents Attractor and its dimension estimation Inertial manifold The approximate inertial manifold
Автор: Guo Boling, Ling Liming, Ma Yansheng Название: Attractors and Methods ISBN: 3110586991 ISBN-13(EAN): 9783110586992 Издательство: Walter de Gruyter Цена: 40403.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
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
Описание: The primary readership includes graduate and PhD students and researchers in in the field of dynamical systems and their applications (control theory, economic dynamics, mathematical theory of climate, population dynamics, oscillation theory etc).
Описание: The primary readership includes graduate and PhD students and researchers in in the field of dynamical systems and their applications (control theory, economic dynamics, mathematical theory of climate, population dynamics, oscillation theory etc).
Описание: 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.
Автор: Alexandre Carvalho; Jos? A. Langa; James Robinson Название: Attractors for infinite-dimensional non-autonomous dynamical systems ISBN: 148999176X ISBN-13(EAN): 9781489991768 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This treatment of pull-back attractors for non-autonomous Dynamical systems emphasizes the infinite-dimensional variety but also analyzes those that are finite. As a graduate primer, it covers everything from basic definitions to cutting-edge results.
Описание: The theory of semigroups of operators is a topic with great intellectual beauty and wide-ranging applications. This graduate-level introduction presents the essential elements of the theory, introducing the key notions and establishing the central theorems. A mixture of applications are included and further development directions are indicated.
Автор: Batkai, Andras , Piazzera, Susanna Название: Semigroups for Delay Equations ISBN: 0367454165 ISBN-13(EAN): 9780367454166 Издательство: Taylor&Francis Рейтинг: Цена: 9492.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book describes how to construct the solutions of the delay equation from the semigroup associated to the equivalent abstract Cauchy problem. It considers parabolic problems with delays in the highest order derivatives and discusses abstract delay equations on a Banach space.
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