Document Server@UHasselt >
Research publications >
Please use this identifier to cite or link to this item:
|Title: ||ON THE SADDLE LOOP BIFURCATION|
|Authors: ||DUMORTIER, Freddy|
|Issue Date: ||1990|
|Publisher: ||SPRINGER VERLAG|
|Citation: ||LECTURE NOTES IN MATHEMATICS, 1455. p. 44-73|
|Abstract: ||It is shown that the set of C-infinity (generic) saddle loop bifurcations has a unique modulus of stability gamma epsilon]0, 1[union cup]1, infinity[ for (C(o), C(r))-equivalence, with 1 less-than-or-equal-to r less-than-or-equal-to infinity. We mean for an equivalence (x,mu) --> (h(x,mu), psi(mu)) with h continuous and psi of class C(r). The modulus gamma is the ratio of hyperbolicity at the saddle point of the connection. Already asking psi to be a lipeomorphism forces two saddle loop bifurcations to have the same modulus, while two such bifurcations with the same modulus are (C(o), +/- Identity)-equivalent. A side result states that the Poincare map of the connection is C1-conjugate to the mapping x --> x-gamma. In the last part of the paper is shown how to finish the proof that the Bogdanov-Takens bifurcation has exactly two models for (C(o), C-infinity)-equivalence.|
|Notes: ||UNIV BOURGOGNE,DEPT MATH,UFR SCI & TECH,TOPOL LAB,CNRS,UA 755,F-21004 DIJON,FRANCE.DUMORTIER, F, LIMBURGS UNIV CENTRUM,UNIV CAMPUS,B-3610 DIEPENBEEK,BELGIUM.|
|ISI #: ||A1990FH64000003|
|Type: ||Journal Contribution|
|Appears in Collections: ||Research publications|
Files in This Item:
There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.