Period-doubling cascades for large perturbations of Henon families

Details Period-doubling cascades for large perturbations of Henon families Period-doubling cascades for large perturbations of Henon families

2009-03-20

arxiv.org/abs/0903.3607v2

Mathematics

Dynamical Systems

14 pages; improved exposition

Scientific paper

10.1007/s11784-009-0116-7

The Henon family has been shown to have period-doubling cascades. We show here that the same occurs for a much larger class: Large perturbations do not destroy cascades. Furthermore, we can classify the period of a cascade in terms of the set of orbits it contains, and count the number of cascades of each period. This class of families extends a general theory explaining why cascades occur.

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