Download or read book Qualitative Theory of Planar Differential Systems written by Freddy Dumortier and published by Springer Science & Business Media. This book was released on 2006-10-13 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with systems of polynomial autonomous ordinary differential equations in two real variables. The emphasis is mainly qualitative, although attention is also given to more algebraic aspects as a thorough study of the center/focus problem and recent results on integrability. In the last two chapters the performant software tool P4 is introduced. From the start, differential systems are represented by vector fields enabling, in full strength, a dynamical systems approach. All essential notions, including invariant manifolds, normal forms, desingularization of singularities, index theory and limit cycles, are introduced and the main results are proved for smooth systems with the necessary specifications for analytic and polynomial systems.

Download or read book Introduction to the Qualitative Theory of Differential Systems written by Jaume Llibre and published by Springer Science & Business Media. This book was released on 2013-10-30 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with continuous piecewise linear differential systems in the plane with three pieces separated by a pair of parallel straight lines. Moreover, these differential systems are symmetric with respect to the origin of coordinates. This class of systems driven by concrete applications is of interest in engineering, in particular in control theory and the design of electric circuits. By studying these particular differential systems we will introduce the basic tools of the qualitative theory of ordinary differential equations, which allow us to describe the global dynamics of these systems including the infinity. The behavior of their solutions, their parametric stability or instability and their bifurcations are described. The book is very appropriate for a first course in the qualitative theory of differential equations or dynamical systems, mainly for engineers, mathematicians, and physicists.

Download or read book Qualitative Theory of Differential Equations written by Zhifen Zhang and published by American Mathematical Soc.. This book was released on 1992 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Subriemannian geometries, also known as Carnot-Caratheodory geometries, can be viewed as limits of Riemannian geometries. They also arise in physical phenomenon involving ``geometric phases'' or holonomy. Very roughly speaking, a subriemannian geometry consists of a manifold endowed with a distribution (meaning a $k$-plane field, or subbundle of the tangent bundle), called horizontal together with an inner product on that distribution. If $k=n$, the dimension of the manifold, we get the usual Riemannian geometry. Given a subriemannian geometry, we can define the distance between two points just as in the Riemannian case, except we are only allowed to travel along the horizontal lines between two points. The book is devoted to the study of subriemannian geometries, their geodesics, and their applications. It starts with the simplest nontrivial example of a subriemannian geometry: the two-dimensional isoperimetric problem reformulated as a problem of finding subriemannian geodesics. Among topics discussed in other chapters of the first part of the book the author mentions an elementary exposition of Gromov's surprising idea to use subriemannian geometry for proving a theorem in discrete group theory and Cartan's method of equivalence applied to the problem of understanding invariants (diffeomorphism types) of distributions. There is also a chapter devoted to open problems. The second part of the book is devoted to applications of subriemannian geometry. In particular, the author describes in detail the following four physical problems: Berry's phase in quantum mechanics, the problem of a falling cat righting herself, that of a microorganism swimming, and a phase problem arising in the $N$-body problem. He shows that all these problems can be studied using the same underlying type of subriemannian geometry: that of a principal bundle endowed with $G$-invariant metrics. Reading the book requires introductory knowledge of differential geometry, and it can serve as a good introduction to this new, exciting area of mathematics. This book provides an introduction to and a comprehensive study of the qualitative theory of ordinary differential equations. It begins with fundamental theorems on existence, uniqueness, and initial conditions, and discusses basic principles in dynamical systems and Poincare-Bendixson theory. The authors present a careful analysis of solutions near critical points of linear and nonlinear planar systems and discuss indices of planar critical points. A very thorough study of limit cycles is given, including many results on quadratic systems and recent developments in China. Other topics included are: the critical point at infinity, harmonic solutions for periodic differential equations, systems of ordinary differential equations on the torus, and structural stability for systems on two-dimensional manifolds. This books is accessible to graduate students and advanced undergraduates and is also of interest to researchers in this area. Exercises are included at the end of each chapter.

Download or read book Approaches To The Qualitative Theory Of Ordinary Differential Equations Dynamical Systems And Nonlinear Oscillations written by Ding Tong-ren and published by World Scientific Publishing Company. This book was released on 2007-08-13 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an ideal text for advanced undergraduate students and graduate students with an interest in the qualitative theory of ordinary differential equations and dynamical systems. Elementary knowledge is emphasized by the detailed discussions on the fundamental theorems of the Cauchy problem, fixed-point theorems (especially the twist theorems), the principal idea of dynamical systems, the nonlinear oscillation of Duffing's equation, and some special analyses of particular differential equations. It also contains the latest research by the author as an integral part of the book.

Download or read book Qualitative Theory of Differential Equations written by V. V. Nemytskii and published by Courier Corporation. This book was released on 1989-01-01 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate-level text considers existence and continuity theorems, integral curves of a system of 2 differential equations, systems of n-differential equations, general theory of dynamical systems, systems with an integral invariant, more. 1960 edition.

Download or read book A First Course in the Qualitative Theory of Differential Equations written by James Hetao Liu and published by . This book was released on 2003 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a complete analysis of those subjects that are of fundamental importance to the qualitative theory of differential equations and related to current research-including details that other books in the field tend to overlook. Chapters 1-7 cover the basic qualitative properties concerning existence and uniqueness, structures of solutions, phase portraits, stability, bifurcation and chaos. Chapters 8-12 cover stability, dynamical systems, and bounded and periodic solutions. A good reference book for teachers, researchers, and other professionals.

Download or read book Planar Dynamical Systems written by Yirong Liu and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-10-29 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 2008, November 23-28, the workshop of ”Classical Problems on Planar Polynomial Vector Fields ” was held in the Banff International Research Station, Canada. Called "classical problems", it was concerned with the following: (1) Problems on integrability of planar polynomial vector fields. (2) The problem of the center stated by Poincaré for real polynomial differential systems, which asks us to recognize when a planar vector field defined by polynomials of degree at most n possesses a singularity which is a center. (3) Global geometry of specific classes of planar polynomial vector fields. (4) Hilbert’s 16th problem. These problems had been posed more than 110 years ago.Therefore, they are called "classical problems" in the studies of the theory of dynamical systems. The qualitative theory and stability theory of differential equations, created by Poincaré and Lyapunov at the end of the 19th century, had major developments as two branches of the theory of dynamical systems during the 20th century. As a part of the basic theory of nonlinear science, it is one of the very active areas in the new millennium. This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert’s 16th problem. The book is intended for graduate students, post-doctors and researchers in dynamical systems. For all engineers who are interested in the theory of dynamical systems, it is also a reasonable reference. It requires a minimum background of a one-year course on nonlinear differential equations.

Download or read book The Qualitative Theory of Ordinary Differential Equations written by Fred Brauer and published by Courier Corporation. This book was released on 2012-12-11 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Superb, self-contained graduate-level text covers standard theorems concerning linear systems, existence and uniqueness of solutions, and dependence on parameters. Focuses on stability theory and its applications to oscillation phenomena, self-excited oscillations, more. Includes exercises.

Download or read book Ordinary Differential Equations written by Luis Barreira and published by American Mathematical Soc.. This book was released on 2012-06-06 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a comprehensive introduction to the qualitative theory of ordinary differential equations. It includes a discussion of the existence and uniqueness of solutions, phase portraits, linear equations, stability theory, hyperbolicity and equations in the plane. The emphasis is primarily on results and methods that allow one to analyze qualitative properties of the solutions without solving the equations explicitly. The text includes numerous examples that illustrate in detail the new concepts and results as well as exercises at the end of each chapter. The book is also intended to serve as a bridge to important topics that are often left out of a course on ordinary differential equations. In particular, it provides brief introductions to bifurcation theory, center manifolds, normal forms and Hamiltonian systems.

Download or read book Qualitative Theory of Differential Equations written by Viktor Vladimirovich Nemytskii and published by Princeton University Press. This book was released on 2015-12-08 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Book 22 in the Princeton Mathematical Series. Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Download or read book Geometric Configurations of Singularities of Planar Polynomial Differential Systems written by Joan C. Artés and published by Springer Nature. This book was released on 2021-07-19 with total page 699 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the global study of finite and infinite singularities of planar polynomial differential systems, with special emphasis on quadratic systems. While results covering the degenerate cases of singularities of quadratic systems have been published elsewhere, the proofs for the remaining harder cases were lengthier. This book covers all cases, with half of the content focusing on the last non-degenerate ones. The book contains the complete bifurcation diagram, in the 12-parameter space, of global geometrical configurations of singularities of quadratic systems. The authors’ results provide - for the first time - global information on all singularities of quadratic systems in invariant form and their bifurcations. In addition, a link to a very helpful software package is included. With the help of this software, the study of the algebraic bifurcations becomes much more efficient and less time-consuming. Given its scope, the book will appeal to specialists on polynomial differential systems, pure and applied mathematicians who need to study bifurcation diagrams of families of such systems, Ph.D. students, and postdoctoral fellows.

Download or read book Ordinary Differential Equations written by Jane Cronin and published by CRC Press. This book was released on 1994-02-15 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text, now in its second edition, presents the basic theory of ordinary differential equations and relates the topological theory used in differential equations to advanced applications in chemistry and biology. It provides new motivations for studying extension theorems and existence theorems, supplies real-world examples, gives an early introduction to the use of geometric methods and offers a novel treatment of the Sturm-Liouville theory.

Download or read book Methods of Qualitative Theory of Differential Equations and Related Topics written by Lev M. Lerman and published by American Mathematical Soc.. This book was released on 2000 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dedicated to the memory of Professor E. A. Leontovich-Andronova, this book was composed by former students and colleagues who wished to mark her contributions to the theory of dynamical systems. A detailed introduction by Leontovich-Andronova's close colleague, L. Shilnikov, presents biographical data and describes her main contribution to the theory of bifurcations and dynamical systems. The main part of the volume is composed of research papers presenting the interests of Leontovich-Andronova, her students and her colleagues. Included are articles on traveling waves in coupled circle maps, bifurcations near a homoclinic orbit, polynomial quadratic systems on the plane, foliations on surfaces, homoclinic bifurcations in concrete systems, topology of plane controllability regions, separatrix cycle with two saddle-foci, dynamics of 4-dimensional symplectic maps, torus maps from strong resonances, structure of 3 degree-of-freedom integrable Hamiltonian systems, splitting separatrices in complex differential equations, Shilnikov's bifurcation for C1-smooth systems and "blue sky catastrophe" for periodic orbits.

Download or read book Qualitative Theory of Hybrid Dynamical Systems written by Alexey S. Matveev and published by Springer Science & Business Media. This book was released on 2000-03-23 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emerging area of hybrid dynamical systems lies at the interface of control theory and computer science, i.e., analogue 'and' digital aspects of systems. This new monograph presents state-of-the-art concepts, methods and tools for analyzing and describing hybrid dynamical systems.

Download or read book Qualitative Theory of Dynamical Systems written by Luo Dingjun and published by World Scientific. This book was released on 1993-09-21 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the global qualitative behavior of flows and diffeomorphisms. It presents a systematic study of the fundamental theory and method of dynamical systems, from local behavior near a critical (fixed) point or periodic orbit to the global, such as global structural stability, bifurcations and chaos. It emphasizes the global non-hyperbolicity and introduces some new results obtained by Chinese mathematicians which may not be widely known. Contents:Preparations of Differentiable Manifolds and Differential TopologyDynamical Systems on ManifoldsLocal Properties of Flows and DiffeomophismsStructural Stability and BifurcationsChaotic BehaviorGeneric Properties Readership: Pure and applied mathematicians and applied scientists. keywords: “… a clear and easy-to-read introduction to dynamical systems in which one can find many definitions, much information and also some important proofs.” Mathematical Reviews “The style of the book is brief and compact, and the selected materials are lucid and refined. Each topic is stated clearly from the simple to the profound. This book can serve both as an easy-reading introduction to the study field of dynamical systems for the beginner and as a valuable reference for the specialists.” Mathematics Abstracts

Download or read book ORDINARY DIFFERENTIAL EQUATIONS written by JANE. CRONIN and published by . This book was released on 2023 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Qualitative Theory of Dynamical Systems written by Anthony Michel and published by CRC Press. This book was released on 2001-01-04 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Illuminates the most important results of the Lyapunov and Lagrange stability theory for a general class of dynamical systems by developing topics in a metric space independantly of equations, inequalities, or inclusions. Applies the general theory to specific classes of equations. Presents new and expanded material on the stability analysis of hybrid dynamical systems and dynamical systems with discontinuous dynamics."