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Nome campo	dettagli
Dewey Class	515
Titolo	Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem ([EBook] /) / by Robert Roussarie.
Autore	Roussarie, Robert
Other name(s)	SpringerLink (Online service)
Edition statement	1998. Reprint 2013 of the 1998 edition.
Pubblicazione	Basel : : Springer Basel : : Imprint: Birkhäuser, , 1998.
Physical Details	XVII, 206 p. : online resource.
Serie	Modern Birkhäuser classics 2197-1803
ISBN	9783034807180
Summary Note	In a coherent, exhaustive and progressive way, this book presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. A systematic introduction is given to such methods as division of an analytic family of functions in its ideal of coefficients, and asymptotic expansion of non-differentiable return maps and desingularisation. The exposition moves from classical analytic geometric methods applied to regular limit periodic sets to more recent tools for singular limit sets. The methods can be applied to theoretical problems such as Hilbert's 16th problem, but also for the purpose of establishing bifurcation diagrams of specific families as well as explicit computations. - - - The book as a whole is a well-balanced exposition that can be recommended to all those who want to gain a thorough understanding and proficiency in recently developed methods. The book, reflecting the state of the art, can also be used for teaching special courses. (Mathematical Reviews) .:
Contents note	Preface -- 1 Families of Two-dimensional Vector Fields -- 2 Limit Periodic Sets -- 3 The 0-Parameter Case -- 4 Bifurcations of Regular Limit Periodic Sets -- 5 Bifurcations of Elementary Graphics -- 6 Desingularization Theory and Bifurcation of Non-elementary Limit Periodic Sets -- Bibliography -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-0348-0718-0
Link alle Opere Legate	Riferimenti soggetto: . Analysis . Analysis (Mathematics) . Dynamical systems and ergodic theory . Dynamics . Ergodic theory . Global Analysis and Analysis on Manifolds . Global analysis (Mathematics) . Manifolds (Mathematics) . Mathematical analysis . Mathematics . Partial differential equations . Authors: Roussarie, Robert . Corporate Authors: SpringerLink (Online service) . Series: Modern Birkhäuser classics . Classification: 515 .

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Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem

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