The isolated saddle-node bifurcation occurring inside a horseshoe

Details The isolated saddle-node bifurcation occurring inside a horseshoe The isolated saddle-node bifurcation occurring inside a horseshoe

1998-10-19

arxiv.org/abs/math/9810118v1

Mathematics

Dynamical Systems

18 pages, 4 figures, to apper Dynamics and Stability of Systems

Scientific paper

In this paper, we consider a smooth arc of diffeomorphisms which has a saddle-node bifurcation inside a nontrivial invariant set which is a deformation of a horseshoe. We show that this saddle-node bifurcation is isolated, that is, its hyperbolicity is maintained before and after the saddle-node bifurcation. Moreover we construct a $C^2$-open set of arcs having the same property.

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