Uniqueness of Limit Cycles in Polynomial Systems with Algebraic Invariants PDF Download

Author: André Zegeling
Publisher:
ISBN:
Category :
Languages : en
Pages : 34

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Author:
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ISBN:
Category : Aeronautics
Languages : en
Pages : 384

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Author: Henryk Zoladek
Publisher: Springer Science & Business Media
ISBN: 3764375361
Category : Mathematics
Languages : en
Pages : 589

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In singularity theory and algebraic geometry, the monodromy group is embodied in the Picard-Lefschetz formula and the Picard-Fuchs equations. It has applications in the weakened 16th Hilbert problem and in mixed Hodge structures. There is a deep connection of monodromy theory with Galois theory of differential equations and algebraic functions. In covering these and other topics, this book underlines the unifying role of the monogropy group.

Author: Freddy Dumortier
Publisher: Springer Science & Business Media
ISBN: 3540329021
Category : Mathematics
Languages : en
Pages : 309

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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.

Author: Xiang Zhang
Publisher: Springer
ISBN: 9811042268
Category : Mathematics
Languages : en
Pages : 390

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This is the first book to systematically state the fundamental theory of integrability and its development of ordinary differential equations with emphasis on the Darboux theory of integrability and local integrability together with their applications. It summarizes the classical results of Darboux integrability and its modern development together with their related Darboux polynomials and their applications in the reduction of Liouville and elementary integrabilty and in the center—focus problem, the weakened Hilbert 16th problem on algebraic limit cycles and the global dynamical analysis of some realistic models in fields such as physics, mechanics and biology. Although it can be used as a textbook for graduate students in dynamical systems, it is intended as supplementary reading for graduate students from mathematics, physics, mechanics and engineering in courses related to the qualitative theory, bifurcation theory and the theory of integrability of dynamical systems.

Author: Joan C. Artés
Publisher: Springer Nature
ISBN: 3030505707
Category : Mathematics
Languages : en
Pages : 699

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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.

Author: A. Canada
Publisher: Elsevier
ISBN: 0080532829
Category : Mathematics
Languages : en
Pages : 709

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The book contains seven survey papers about ordinary differential equations.The common feature of all papers consists in the fact that nonlinear equations are focused on. This reflects the situation in modern mathematical modelling - nonlinear mathematical models are more realistic and describe the real world problems more accurately. The implications are that new methods and approaches have to be looked for, developed and adopted in order to understand and solve nonlinear ordinary differential equations.The purpose of this volume is to inform the mathematical community and also other scientists interested in and using the mathematical apparatus of ordinary differential equations, about some of these methods and possible applications.

Author: D. Bainov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3112319184
Category : Mathematics
Languages : en
Pages : 480

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No detailed description available for "Proceedings of the seventh International Colloquium on Differential Equations".

Author: Yanqian Ye
Publisher: American Mathematical Soc.
ISBN: 9780821845189
Category : Mathematics
Languages : en
Pages : 452

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Deals with limit cycles of general plane stationary systems, including their existence, nonexistence, stability, and uniqueness. This book also discusses the global topological structure of limit cycles and phase-portraits of quadratic systems.

Author:
Publisher:
ISBN:
Category : Mathematical analysis
Languages : en
Pages : 1104

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