Institute for Mathematical Sciences

Preprint ims10-01

P. E. Hazard
Henon-like maps with arbitrary stationary combinatorics

Abstract: We extend the renormalization operator introduced in [3] from period-doubling Henon-like maps to Henon-like maps with arbitrary stationary combinatorics. We show the renormalisation prodcudure also holds in this case if the maps are taken to be strongly dissipative. We study infinitely renormalizable maps F and show they have an invariant Cantor set O on which F acts like a p-adic adding machine for some p > 1. We then show, as for the period-doubling case in [3], the sequence of renormalisations have a universal form, but the invariant Cantor set O is non-rigid. We also show O cannot possess a continuous invariant line field.
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