Dynamical Systems By Example
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Dynamical Systems By Example
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Author : Luís Barreira
language : en
Publisher: Springer
Release Date : 2019-04-17
Dynamical Systems By Example written by Luís Barreira and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-17 with Mathematics categories.
This book comprises an impressive collection of problems that cover a variety of carefully selected topics on the core of the theory of dynamical systems. Aimed at the graduate/upper undergraduate level, the emphasis is on dynamical systems with discrete time. In addition to the basic theory, the topics include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as basic ergodic theory. As in other areas of mathematics, one can gain the first working knowledge of a topic by solving selected problems. It is rare to find large collections of problems in an advanced field of study much less to discover accompanying detailed solutions. This text fills a gap and can be used as a strong companion to an analogous dynamical systems textbook such as the authors’ own Dynamical Systems (Universitext, Springer) or another text designed for a one- or two-semester advanced undergraduate/graduate course. The book is also intended for independent study. Problems often begin with specific cases and then move on to general results, following a natural path of learning. They are also well-graded in terms of increasing the challenge to the reader. Anyone who works through the theory and problems in Part I will have acquired the background and techniques needed to do advanced studies in this area. Part II includes complete solutions to every problem given in Part I with each conveniently restated. Beyond basic prerequisites from linear algebra, differential and integral calculus, and complex analysis and topology, in each chapter the authors recall the notions and results (without proofs) that are necessary to treat the challenges set for that chapter, thus making the text self-contained.
Dynamical Systems
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Author : Luis Barreira
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-02
Dynamical Systems written by Luis Barreira 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 2012-12-02 with Mathematics categories.
The theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics. Dynamical Systems: An Introduction undertakes the difficult task to provide a self-contained and compact introduction. Topics covered include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as a brief introduction to ergodic theory. In particular, the authors consider topological recurrence, topological entropy, homeomorphisms and diffeomorphisms of the circle, Sharkovski's ordering, the Poincaré-Bendixson theory, and the construction of stable manifolds, as well as an introduction to geodesic flows and the study of hyperbolicity (the latter is often absent in a first introduction). Moreover, the authors introduce the basics of symbolic dynamics, the construction of symbolic codings, invariant measures, Poincaré's recurrence theorem and Birkhoff's ergodic theorem. The exposition is mathematically rigorous, concise and direct: all statements (except for some results from other areas) are proven. At the same time, the text illustrates the theory with many examples and 140 exercises of variable levels of difficulty. The only prerequisites are a background in linear algebra, analysis and elementary topology. This is a textbook primarily designed for a one-semester or two-semesters course at the advanced undergraduate or beginning graduate levels. It can also be used for self-study and as a starting point for more advanced topics.
Dynamical Systems
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Author : Jürgen Jost
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-24
Dynamical Systems written by Jürgen Jost 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 2005-11-24 with Science categories.
Breadth of scope is unique Author is a widely-known and successful textbook author Unlike many recent textbooks on chaotic systems that have superficial treatment, this book provides explanations of the deep underlying mathematical ideas No technical proofs, but an introduction to the whole field that is based on the specific analysis of carefully selected examples Includes a section on cellular automata
Dynamic Systems
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Author : Craig A. Kluever
language : en
Publisher: John Wiley & Sons
Release Date : 2020-06-23
Dynamic Systems written by Craig A. Kluever and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-23 with Technology & Engineering categories.
The simulation of complex, integrated engineering systems is a core tool in industry which has been greatly enhanced by the MATLAB® and Simulink® software programs. The second edition of Dynamic Systems: Modeling, Simulation, and Control teaches engineering students how to leverage powerful simulation environments to analyze complex systems. Designed for introductory courses in dynamic systems and control, this textbook emphasizes practical applications through numerous case studies—derived from top-level engineering from the AMSE Journal of Dynamic Systems. Comprehensive yet concise chapters introduce fundamental concepts while demonstrating physical engineering applications. Aligning with current industry practice, the text covers essential topics such as analysis, design, and control of physical engineering systems, often composed of interacting mechanical, electrical, and fluid subsystem components. Major topics include mathematical modeling, system-response analysis, and feedback control systems. A wide variety of end-of-chapter problems—including conceptual problems, MATLAB® problems, and Engineering Application problems—help students understand and perform numerical simulations for integrated systems.
Linear Dynamical Systems
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Author : Mircea D. Grigoriu
language : en
Publisher: Springer Nature
Release Date : 2021-01-30
Linear Dynamical Systems written by Mircea D. Grigoriu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-30 with Science categories.
This textbook provides a concise, clear, and rigorous presentation of the dynamics of linear systems that delivers the necessary tools for the analysis and design of mechanical/ structural systems, regardless of their complexity. The book is written for senior undergraduate and first year graduate students as well as engineers working on the design of mechanical/structural systems subjected to dynamic actions, such as wind/earthquake engineers and mechanical engineers working on wind turbines. Professor Grigoriu's lucid presentation maximizes student understanding of the formulation and the solution of linear systems subjected to dynamic actions, and provides a clear distinction between problems of practical interest and their special cases. Based on the author's lecture notes from courses taught at Cornell University, the material is class-tested over many years and ideal as a core text for a range of classes in mechanical, civil, and geotechnical engineering, as well as for self-directed learning by practitioners in the field.
Modeling And Simulation Of Dynamical Systems
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Author : Payam Zarafshan
language : en
Publisher: Elsevier
Release Date : 2024-11-27
Modeling And Simulation Of Dynamical Systems written by Payam Zarafshan and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-27 with Technology & Engineering categories.
Modeling and Simulation of Dynamical Systems explores the common methods used in the modeling and simulation of dynamic systems, providing foundational information that is essential for further research. A key feature of this title is its systematic separation and classification of various modeling methods, enabling readers to select their preferred approach after studying the initial chapter and becoming familiar with fundamental definitions. Another unique feature is the use of numerous examples and solved problems throughout the book to support a basic understanding of a system's behavior.This title is highly recommended for researchers, professionals, and students in mechanical, biosystems, and mechatronic engineering. - Explores, in detail, the different methods of modeling dynamic systems - Provides numerous examples and solved problems, which distinguishes this book from other reference titles in the field - Renders information on modeling and simulating software
Neural Network Modeling And Identification Of Dynamical Systems
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Author : Yury Tiumentsev
language : en
Publisher: Academic Press
Release Date : 2019-05-17
Neural Network Modeling And Identification Of Dynamical Systems written by Yury Tiumentsev and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-17 with Science categories.
Neural Network Modeling and Identification of Dynamical Systems presents a new approach on how to obtain the adaptive neural network models for complex systems that are typically found in real-world applications. The book introduces the theoretical knowledge available for the modeled system into the purely empirical black box model, thereby converting the model to the gray box category. This approach significantly reduces the dimension of the resulting model and the required size of the training set. This book offers solutions for identifying controlled dynamical systems, as well as identifying characteristics of such systems, in particular, the aerodynamic characteristics of aircraft. - Covers both types of dynamic neural networks (black box and gray box) including their structure, synthesis and training - Offers application examples of dynamic neural network technologies, primarily related to aircraft - Provides an overview of recent achievements and future needs in this area
Integrability And Nonintegrability Of Dynamical Systems
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Author : Alain Goriely
language : en
Publisher: World Scientific
Release Date : 2001-08-29
Integrability And Nonintegrability Of Dynamical Systems written by Alain Goriely and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-08-29 with Science categories.
This invaluable book examines qualitative and quantitative methods for nonlinear differential equations, as well as integrability and nonintegrability theory. Starting from the idea of a constant of motion for simple systems of differential equations, it investigates the essence of integrability, its geometrical relevance and dynamical consequences. Integrability theory is approached from different perspectives, first in terms of differential algebra, then in terms of complex time singularities and finally from the viewpoint of phase geometry (for both Hamiltonian and non-Hamiltonian systems). As generic systems of differential equations cannot be exactly solved, the book reviews the different notions of nonintegrability and shows how to prove the nonexistence of exact solutions and/or a constant of motion. Finally, nonintegrability theory is linked to dynamical systems theory by showing how the property of complete integrability, partial integrability or nonintegrability can be related to regular and irregular dynamics in phase space.
Dynamical Systems
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Author : Lamberto Cesari
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Dynamical Systems written by Lamberto Cesari and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Dynamical Systems: An International Symposium, Volume 2 contains the proceedings of the International Symposium on Dynamical Systemsheld at Brown University in Providence, Rhode Island, on August 12-16, 1974. The symposium provided a forum for reviewing the theory of dynamical systems in relation to ordinary and functional differential equations, as well as the influence of this approach and the techniques of ordinary differential equations on research concerning certain types of partial differential equations and evolutionary equations in general. Comprised of six chapters, this volume first examines how the theory of isolating blocks may be applied to the Newtonian planar three-body problem. The reader is then introduced to the separatrix structure for regions attracted to solitary periodic solutions; solitary invariant sets; and singular points and separatrices. Subsequent chapters focus on the equivalence of suspensions and manifolds with cross section; a geometrical approach to classical mechanics; bifurcation theory for odd potential operators; and continuous dependence of fixed points of condensing maps. This monograph will be of interest to students and practitioners in the field of applied mathematics.
Dynamical Systems Based Soil Mechanics
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Author : Paul Joseph
language : en
Publisher: CRC Press
Release Date : 2017-04-24
Dynamical Systems Based Soil Mechanics written by Paul Joseph and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-24 with Technology & Engineering categories.
This book is a short yet rigorous course on a new paradigm in soil mechanics, one that holds that soil deformation occurs as a simple friction-based Poisson process in which soil particles move to their final position at random shear strains. It originates from work by Casagrande’s soil mechanics group at Harvard University that found that an aggregate of soil particles when sheared reaches a "steady-state" condition, a finding in line with the thermodynamics of dissipative systems. The book unpacks this new paradigm as it applies to soils. The theory explains fundamental, ubiquitous soil behaviors and relationships used in soils engineering daily thousands of times across the world, but whose material bases so far have been unknown. These include for example, why for one-dimensional consolidation, the e-log σ line is linear, and why Cα/Cc is a constant for a given soil. The subtext of the book is that with this paradigm, the scientific method of trying to falsify hypotheses fully drives advances in the field, i.e., that soil mechanics now strictly qualifies as a science that, in turn, informs geotechnical engineering. The audience for the book is senior undergraduates, graduate students, academics, and researchers as well as industry professionals, particularly geotechnical engineers. It will also be useful to structural engineers, highway engineers, military engineers, persons in the construction industry, as well as planetary scientists. Because its fundamental findings hold for any mass of particles like soils, the theory applies not just to soils, but also to powders, grains etc. so long as these are under pseudo-static (no inertial effects) conditions.