Saddle-nodes and period-doublings of Smale horseshoes: A case study near resonant homoclinic bellows

Authors
Publication date 2008
Journal Bulletin of the Belgian Mathematical Society - Simon Stevin
Volume | Issue number 15 | 5
Pages (from-to) 833-850
Organisations
  • Faculty of Science (FNWI) - Korteweg-de Vries Institute for Mathematics (KdVI)
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".
Document type Article
Published at http://projecteuclid.org/euclid.bbms/1228486411
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