Bulletin of the Belgian Mathematical Society - Simon Stevin

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

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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''.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 15, Number 5 (2008), 833-850.

Dates
First available in Project Euclid: 5 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1228486411

Digital Object Identifier
doi:10.36045/bbms/1228486411

Mathematical Reviews number (MathSciNet)
MR2484136

Zentralblatt MATH identifier
1160.37018

Subjects
Primary: 37G20: Hyperbolic singular points with homoclinic trajectories 37G30: Infinite nonwandering sets arising in bifurcations

Keywords
homoclinic loop horseshoe bifurcation

Citation

Homburg, Ale Jan; Jukes, Alice C.; Knobloch, Jürgen; Lamb, Jeroen S.W. Saddle-nodes and period-doublings of Smale horseshoes: a case study near resonant homoclinic bellows. Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 5, 833--850. doi:10.36045/bbms/1228486411. https://projecteuclid.org/euclid.bbms/1228486411


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