Abstract

We present and explain numerical results illustrating the mechanism of a type of discontinuous bifurcation of a chaotic set that occurs in typical dynamical systems. After the bifurcation, the chaotic set acquires new pieces located at a finite distance from its location just before the bifurcation, and these new pieces were not part of a previously existing chaotic set. A scaling law is given describing the creation of unstable periodic orbits following such a bifurcation. We also provide numerical evidence of such a bifurcation for a nonattracting chaotic set of the H\'enon map.

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