## Bulletin of the Belgian Mathematical Society - Simon Stevin

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

#### 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