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Author : Sergei Yu. Pilyugin
Publisher : Walter de Gruyter GmbH & Co KG
Page : 379 pages
File Size : 53,8 Mb
Release : 2019-08-05
Category : Science
ISBN : 9783110653991
Author : Sergei Yu. Pilyugin
Publisher : Springer
Page : 197 pages
File Size : 49,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540483144
This book is an introduction to main methods and principal results in the theory of Co(remark: o is upper index!!)-small perturbations of dynamical systems. It is the first comprehensive treatment of this topic. In particular, Co(upper index!)-generic properties of dynamical systems, topological stability, perturbations of attractors, limit sets of domains are discussed. The book contains some new results (Lipschitz shadowing of pseudotrajectories in structurally stable diffeomorphisms for instance). The aim of the author was to simplify and to "visualize" some basic proofs, so the main part of the book is accessible to graduate students in pure and applied mathematics. The book will also be a basic reference for researchers in various fields of dynamical systems and their applications, especially for those who study attractors or pseudotrajectories generated by numerical methods.
Author : Sergei Yu. Pilyugin
Publisher : Walter de Gruyter
Page : 244 pages
File Size : 41,9 Mb
Release : 2012-04-10
Category : Science
ISBN : 9783110258417
Dynamical systems are abundant in theoretical physics and engineering. Their understanding, with sufficient mathematical rigor, is vital to solving many problems. This work conveys the modern theory of dynamical systems in a didactically developed fashion. In addition to topological dynamics, structural stability and chaotic dynamics, also generic properties and pseudotrajectories are covered, as well as nonlinearity. The author is an experienced book writer and his work is based on years of teaching.
Author : Aleksandr N. Starkov
Publisher : American Mathematical Soc.
Page : 243 pages
File Size : 54,6 Mb
Release : 2000
Category : Mathematics
ISBN : 0821813897
A homogeneous flow is a dynamical system generated by the action of a closed subgroup $H$ of a Lie group $G$ on a homogeneous space of $G$. The study of such systems is of great significance because they constitute an algebraic model for more general and more complicated systems. Also, there are abundant applications to other fields of mathematics, most notably to number theory. The present book gives an extensive survey of the subject. In the first chapter the author discusses ergodicity and mixing of homogeneous flows. The second chapter is focused on unipotent flows, for which substantial progress has been made during the last 10-15 years. The culmination of this progress was M. Ratner's celebrated proof of far-reaching conjectures of Raghunathan and Dani. The third chapter is devoted to the dynamics of nonunipotent flows. The final chapter discusses applications of homogeneous flows to number theory, mainly to the theory of Diophantine approximations. In particular, the author describes in detail the famous proof of the Oppenheim-Davenport conjecture using ergodic properties of homogeneous flows.
Author : Kuize Zhang,Lijun Zhang,Lihua Xie
Publisher : Springer
Page : 222 pages
File Size : 41,7 Mb
Release : 2019-08-06
Category : Technology & Engineering
ISBN : 9783030259723
Discrete-Time and Discrete-Space Dynamical Systems provides a systematic characterization of the similarities and differences of several types of discrete-time and discrete-space dynamical systems, including: Boolean control networks; nondeterministic finite-transition systems; finite automata; labelled Petri nets; and cellular automata. The book's perspective is primarily based on topological properties though it also employs semitensor-product and graph-theoretic methods where appropriate. It presents a series of fundamental results: invertibility, observability, detectability, reversiblity, etc., with applications to systems biology. Academic researchers with backgrounds in applied mathematics, engineering or computer science and practising engineers working with discrete-time and discrete-space systems will find this book a helpful source of new understanding for this increasingly important class of systems. The basic results to be found within are of fundamental importance for further study of related problems such as automated synthesis and safety control in cyber-physical systems using formal methods.
Author : Sergei Yu. Pilyugin
Publisher : Walter de Gruyter GmbH & Co KG
Page : 256 pages
File Size : 47,6 Mb
Release : 2019-08-05
Category : Science
ISBN : 9783110657166
Author : Sergei Yu. Pilyugin
Publisher : Unknown
Page : 204 pages
File Size : 54,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662213397
Author : Nikolay Kuznetsov,Volker Reitmann
Publisher : Springer Nature
Page : 555 pages
File Size : 49,5 Mb
Release : 2020-07-02
Category : Computers
ISBN : 9783030509873
This book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Carathéodory dimensions) for attractors and invariant sets of dynamical systems and cocycles generated by smooth differential equations or maps in finite-dimensional Euclidean spaces or on manifolds. It also discusses stability investigations using estimates based on Lyapunov functions and adapted metrics. Moreover, it introduces various types of Lyapunov dimensions of dynamical systems with respect to an invariant set, based on local, global and uniform Lyapunov exponents, and derives analytical formulas for the Lyapunov dimension of the attractors of the Hénon and Lorenz systems. Lastly, the book presents estimates of the topological entropy for general dynamical systems in metric spaces and estimates of the topological dimension for orbit closures of almost periodic solutions to differential equations.
Author : Krzysztof Kowalski
Publisher : World Scientific
Page : 148 pages
File Size : 43,7 Mb
Release : 1994
Category : Mathematics
ISBN : 9810217536
This book is the first monograph on a new powerful method discovered by the author for the study of nonlinear dynamical systems relying on reduction of nonlinear differential equations to the linear abstract Schrdinger-like equation in Hilbert space. Besides the possibility of unification of many apparently completely different techniques, the ?quantal? Hilbert space formalism introduced enables new original methods to be discovered for solving nonlinear problems arising in investigation of ordinary and partial differential equations as well as difference equations. Applications covered in the book include symmetries and first integrals, linearization transformations, Bcklund transformations, stroboscopic maps, functional equations involving the case of Feigenbaum-Cvitanovic renormalization equations and chaos.
Author : Wang Sang Koon,Martin W. Lo,Jerrold E. Marsden
Publisher : Springer
Page : 336 pages
File Size : 41,6 Mb
Release : 2011-06-01
Category : Mathematics
ISBN : 0387495150
This book considers global solutions to the restricted three-body problem from a geometric point of view. The authors seek dynamical channels in the phase space which wind around the planets and moons and naturally connect them. These low energy passageways could slash the amount of fuel spacecraft need to explore and develop our solar system. In order to effectively exploit these passageways, the book addresses the global transport. It goes beyond the traditional scope of libration point mission design, developing tools for the design of trajectories which take full advantage of natural three or more body dynamics, thereby saving precious fuel and gaining flexibility in mission planning. This is the key for the development of some NASA mission trajectories, such as low energy libration point orbit missions (e.g., the sample return Genesis Discovery Mission), low energy lunar missions and low energy tours of outer planet moon systems, such as a mission to tour and explore in detail the icy moons of Jupiter. This book can serve as a valuable resource for graduate students and advanced undergraduates in applied mathematics and aerospace engineering, as well as a manual for practitioners who work on libration point and deep space missions in industry and at government laboratories. the authors include a wealth of background material, but also bring the reader up to a portion of the research frontier.
Author : Patricia Mellodge
Publisher : Woodhead Publishing
Page : 292 pages
File Size : 42,5 Mb
Release : 2015-11-19
Category : Mathematics
ISBN : 9780081002247
A Practical Approach to Dynamical Systems for Engineers takes the abstract mathematical concepts behind dynamical systems and applies them to real-world systems, such as a car traveling down the road, the ripples caused by throwing a pebble into a pond, and a clock pendulum swinging back and forth. Many relevant topics are covered, including modeling systems using differential equations, transfer functions, state-space representation, Hamiltonian systems, stability and equilibrium, and nonlinear system characteristics with examples including chaos, bifurcation, and limit cycles. In addition, MATLAB is used extensively to show how the analysis methods are applied to the examples. It is assumed readers will have an understanding of calculus, differential equations, linear algebra, and an interest in mechanical and electrical dynamical systems. Presents applications in engineering to show the adoption of dynamical system analytical methods Provides examples on the dynamics of automobiles, aircraft, and human balance, among others, with an emphasis on physical engineering systems MATLAB and Simulink are used throughout to apply the analysis methods and illustrate the ideas Offers in-depth discussions of every abstract concept, described in an intuitive manner, and illustrated using practical examples, bridging the gap between theory and practice Ideal resource for practicing engineers who need to understand background theory and how to apply it
Author : Sergei Yurievitch Pilyugin
Publisher : Springer
Page : 212 pages
File Size : 51,7 Mb
Release : 1994
Category : Mathematics
ISBN : UCSD:31822017700832
Author : A.A. Coley
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 46,8 Mb
Release : 2013-04-17
Category : Science
ISBN : 9789401703277
Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary differential equations. In this book we discuss cosmological models as dynamical systems, with particular emphasis on applications in the early Universe. We point out the important role of self-similar models. We review the asymptotic properties of spatially homogeneous perfect fluid models in general relativity. We then discuss results concerning scalar field models with an exponential potential (both with and without barotropic matter). Finally, we discuss the dynamical properties of cosmological models derived from the string effective action. This book is a valuable source for all graduate students and professional astronomers who are interested in modern developments in cosmology.
Author : James D. Meiss
Publisher : SIAM
Page : 392 pages
File Size : 45,7 Mb
Release : 2017-01-24
Category : Mathematics
ISBN : 9781611974645
Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.? Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple?, Mathematica?, and MATLAB? software to give students practice with computation applied to dynamical systems problems.
Author : Jan Vries
Publisher : Walter de Gruyter
Page : 513 pages
File Size : 45,8 Mb
Release : 2014-01-31
Category : Mathematics
ISBN : 9783110342406
There is no recent elementary introduction to the theory of discrete dynamical systems that stresses the topological background of the topic. This book fills this gap: it deals with this theory as 'applied general topology'. We treat all important concepts needed to understand recent literature. The book is addressed primarily to graduate students. The prerequisites for understanding this book are modest: a certain mathematical maturity and course in General Topology are sufficient.