02607nmm a2200385 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002200139245011900161250001700280260003800297300003300335505030900368653001900677653004600696653002600742653004100768653003500809653002700844653002800871653003500899653003400934653001300968653001300981710003400994041001901028989003801047490003201085856007201117082000801189520102401197EB000637102EBX0100000000000000049018400000000000000.0cr|||||||||||||||||||||140122 ||| eng a97830348879841 aRoussarie, Robert00aBifurcations of Planar Vector Fields and Hilbert's Sixteenth ProblemhElektronische Ressourcecby Robert Roussarie a1st ed. 1998 aBaselbSpringer Baselc1998, 1998 aXVII, 206 pbonline resource0 aPreface -- 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 aErgodic theory aGlobal Analysis and Analysis on Manifolds aMathematical analysis aDynamical Systems and Ergodic Theory aPartial Differential Equations aAnalysis (Mathematics) aManifolds (Mathematics) aPartial differential equations aGlobal analysis (Mathematics) aAnalysis aDynamics2 aSpringerLink (Online service)07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aModern Birkhäuser Classics uhttps://doi.org/10.1007/978-3-0348-8798-4?nosfx=yxVerlag3Volltext0 a515 aIn 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)