Bifurcations and Periodic Orbits of Vector Fields
By: edited by Dana Schlomiuk
Series: NATO ASI Series, Series C: Mathematical and Physical Sciences -- 408; NATO ASI Series, Series C: Mathematical and Physical Sciences -- 408
Publisher: Springer Netherlands
Published: 1993
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] /
Number of pages: 472
ISBN-13: 9789048143030; 9789401582384
Subjects: Differential Equations; Functions of complex variables; Geometry; Electronic data processing; Sequences (Mathematics); Mathematics; Global analysis
Other titles: Proceedings of the NATO Advanced Study Institute and Séminaire de mathématiques supérieures, Montreal, Canada, July 13-24, 1992
Description: 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 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.
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