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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
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John Guckenheimer, Philip Holmes (Photographer), F John (Editor)
From the reviews: 'This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from ...
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Normal Forms and Bifurcation of Planar Vector Fields
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Chow, Li, Wang
This book is concerned with the bifurcation theory, the study of the changes in the structures of the solution of ordinary differential equations as parameters of the model vary. The theory has developed rapidly over the past two decades. Chapters 1 and 2 of the book introduce two systematic methods of simplifying equations: centre manifold theory ...
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Global Bifurcation Theory and Hilbert's Sixteenth Problem
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Valery A Gaiko
This volume is devoted to the qualitative investigation of two-dimensional polynomial dynamical systems, and is aimed at solving Hilbert's Sixteenth Problem on the maximum number and relative position of limit cycles. The author presents a global bifurcation theory of such systems and suggests a new global approach to the study of limit cycle ...
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Bifurcations of Planar Vector Fields
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Jean-Pierre Francoise (Editor), Robert Roussarie (Editor)
A collection of papers on differential equations and dynamical systems which stresses topics relating to Hilbert's 16th problem. Among these are a solution to Dulac's problem, results on the multiplicity of singular cycles and results on the zeroes of abelian integrals.
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Hypo-Analytic Structures: Local Theory
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Francois Treves
In "Hypo-Analytic Structures" Francois Treves provides a systematic approach to the study of the differential structures on manifolds defined by systems of complex vector fields. Serving as his main examples are the elliptic complexes, among which the De Rham and Dolbeault are the best known and the tangential Cauchy-Riemann operators. Basic ...
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Complex Vector Functional Equations
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Ice Risteski, Valery Covachev
The subject of complex vector functional equations is a new area in the theory of functional equations. This monograph provides a systematic overview of the authors' recently obtained results concerning both linear and nonlinear complex vector functional equations, in all aspects of their utilization. It is intended for mathematicians, physicists ...
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Singularity and Dynamics on Discontinuous Vector Fields
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Albert C J Luo (Editor), George Zaslavsky (Editor)
This book discussed fundamental problems in dynamics, which extensively exist in engineering, natural and social sciences. The book presented a basic theory for the interactions among many dynamical systems and for a system whose motions are constrained naturally or artificially. The methodology and techniques presented in this book are applicable ...
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An Introduction to Involutive Structures
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Paulo D Cordaro, Jorge Hounie, Shiferaw Berhanu
Detailing the main methods in the theory of involutive systems of complex vector fields this book examines the major results from the last twenty five years in the subject. One of the key tools of the subject - the Baouendi-Treves approximation theorem - is proved for many function spaces. This in turn is applied to questions in partial ...
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Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics
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by
Tian Ma
This monograph presents a geometric theory for incompressible flow and its applications to fluid dynamics. The main objective is to study the stability and transitions of the structure of incompressible flows and its applications to fluid dynamics and geophysical fluid dynamics. The development of the theory and its applications goes well beyond ...
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Bifurcations and Periodic Orbits of Vector Fields
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by
Dana Schlomiuk (Editor)
The main topic of this book is the theory of bifurcations of vector fields, i.e. the study of families of vector fields depending on one or several parameters and the changes (bifurcations) in the topological character of the objects studied as parameters vary. In particular, one of the phenomena studied is the bifurcation of periodic orbits from ...
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Vector Fields and Other Vector Bundle Morphisms: A Singularity Approach
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U Koschorke
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Hypoellipticite Maximale Pour Des Operateurs Polynomes de Champs de Vecteurs
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Bernard Helffer
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Bifurcations of Planar Vector Fields: Proceedings of a Meeting Held in Luminy, France, Sept. 18-22, 1989
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J -P Francoise
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Global Aspects of Homoclinic Bifurcations of Vector Fields
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Ale Jan Homburg
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Markov Random Fields
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Iu A Rozanov
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Affine Flows on 3-Manifolds
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by
Robert M Guralnick, Shigenori Matsumoto
In this paper, we consider nonsingular flows on closed 3-manifolds which are transversely modeled on the real affine geometry of the plane. We obtain classification results for the following three types of flows: Flows whose developing maps are $\mathbb{R}$-bundle maps over $\mathbb{R}^2$; Flows whose holonomy groups are contained in $SL(2,\mathbb ...
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Concerning the Hilbert 16th Problem
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by
Iu S Il'iashenko
This book examines qualitative properties of vector fields in the plane, in the spirit of Hilbert's Sixteenth Problem. Two principal topics explored are bifurcations of limit cycles of planar vector fields and desingularization of singular points for individual vector fields and for analytic families of such fields. In addition to presenting ...
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Finiteness Theorems for Limit Cycles
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Yu S. Il'yashenko, Iu S. Il'iashenko
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Structurally Stable Quadratic Vector Fields
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Joan C. Artes, Robert E. Kooij, Jaume Llibre
This book solves a problem that has been open for over 20 years - the complete classification of structurally stable quadratic vector fields modulo limit cycles. The 1950s saw the first real impetus given to the development of the qualitative theory of quadratic vector fields, although prior and ongoing interest in the topic can be shown by the ...
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Continuous Cohomology of the Lie Algebra of Vector Fields
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Toru Tsujishita
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Calculus Visualizing Differential Equations with Slope Fields
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by
Alan Lipp
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Aspects of Complex Analysis, Differentia
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by
Stancho Dimiev (Editor), Kouei Sekigawa (Editor)
This volume constitutes the proceedings of a workshop, the main purpose of which was to provide a forum to exchange information on current topics in complex analysis, differential geometry, mathematical physics and applications, and to group aspects of new mathematics.
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Vector field theory with applications
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by
Leonard Sowerby
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Indices of Vector Fields and Residues of Singular Holomorphic Foliations
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by
T Suwa
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Dynamical systems a differential geometric approach to symmetry and reduction
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by
Marmo
In their discussion of the subject of classical mechanics, the authors of this book use a new and stimulating approach which involves looking at dynamical systems from the viewpoint of differential geometry. They discuss the reduction of these systems, and the role played by symmetry and invariance in such reductions. Central to their approach is ...
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