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OverviewThe 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 a singular point or a polycycle. The following topics are discussed in the book: Divergent series and resummation techniques with applications, in particular to the proofs of the finiteness conjecture of Dulac saying that polynomial vector fields on R2 cannot possess an infinity of limit cycles. The proofs work in the more general context of real analytic vector fields on the plane. Techniques in the study of unfoldings of singularities of vector fields (blowing up, normal forms, desingularization of vector fields). Local dynamics and nonlocal bifurcations. Knots and orbit genealogies in three-dimensional flows. Bifurcations and applications: computational studies of vector fields. Holomorphic differential equations in dimension two. Studies of real and complex polynomial systems and of the complex foliations arising from polynomial differential equations. Applications of computer algebra to dynamical systems. Full Product DetailsAuthor: Dana SchlomiukPublisher: Springer Imprint: Springer Edition: Softcover reprint of hardcover 1st ed. 1993 Volume: 408 Dimensions: Width: 15.50cm , Height: 2.50cm , Length: 23.50cm Weight: 0.753kg ISBN: 9789048143030ISBN 10: 9048143039 Pages: 474 Publication Date: 08 December 2010 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsComplex Foliations Arising from Polynomial Differential Equations.- Techniques in the Theory of Local Bifurcations: Blow-Up, Normal Forms, Nilpotent Bifurcations, Singular Perturbations.- Six Lectures on Transseries, Analysable Functions and the Constructive Proof of Dulac’s Conjecture.- Knots and Orbit Genealogies in Three Dimensional Flows.- Dynamical Systems: Some Computational Problems.- Local Dynamics and Nonlocal Bifurcations.- Singularités d’équations différentielles holomorphes en dimension deux.- Techniques in the Theory of Local Bifurcations: Cyclicity and Desingularization.- Bifurcation Methods in Polynomial Systems.- Algebraic and Geometric Aspects of the Theory of Polynomial Vector Fields.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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