## 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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