Period-doubling cascades for large perturbations of Henon families
arXiv:0903.3607 · doi:10.1007/s11784-009-0116-7
Abstract
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.
14 pages; improved exposition