Saddle-nodes and period-doublings of Smale horseshoes: a case study near resonant homoclinic bellows
Ale Jan Homburg, Alice C. Jukes, Jürgen Knobloch, and Jeroen S.W. Lamb
Source: Bull. Belg. Math. Soc. Simon Stevin Volume 15, Number 5
(2008), 833-850.
Abstract
In unfoldings of resonant homoclinic bellows interesting bifurcation phenomena occur: two suspensed Smale horseshoes can collide and disappear in saddle-node bifurcations (all periodic orbits disappear through saddle-node bifurcations, there are no other bifurcations of periodic orbits), or a suspended horseshoe can go through saddle-node and period-doubling bifurcations of the periodic orbits in it to create an additional ``doubled horseshoe''.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.bbms/1228486411
Zentralblatt MATH identifier: 1160.37018
Mathematical Reviews number (MathSciNet): MR2484136
Bulletin of the Belgian Mathematical Society - Simon Stevin
