Henon-like maps with arbitrary stationary combinatorics

We extend the renormalisation operator introduced in \cite{dCML} from period-doubling H\'enon-like maps to H\'enon-like maps with arbitrary stationary combinatorics. We show the renormalisation picture holds also holds in this case if the maps are taken to be \emph{strongly dissipative}. We study infinitely renormalisable maps $F$ and show they have an invariant Cantor set $\mathcal{O}$ on which $F$ acts like a $p$-adic adding machine for some $p>1$. We then show, as for the period-doubling case in \cite{dCML}, the sequence of renormalisations have a universal form, but the invariant Cantor set $\mathcal{O}$ is non-rigid. We also show $\mathcal{O}$ cannot possess a continuous invariant line field.Comment: 62 pages, 5 figure

Holland, Rogers & Hazard- Mrs. Rosie Holmes Walker, January 13, 1932

Correspondence: Letter from Elmer E. Hazard, Holland Rogers & Hazard Attorneys at Law, Jacksonville, Florida, to Rosa G. Holmes Walker, Jacksonville, Florida, regarding money received on State and County tax sales certificates for property: North half Lot 5, Block 1, Burbridge\u27s Addition to Jacksonville

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Holland, Rogers & Hazard- Mrs. R. H. Walker, August 16, 1932

Correspondence: Letter from Elmer E. Hazard, Holland Rogers & Hazard Attorneys at Law, Jacksonville, Florida, to Rosa G. Holmes Walker, Jacksonville, Florida, regarding money due on State and County tax sales certificate for property: North half Lot 5, Block 1, Burbridge\u27s Addition to Jacksonville

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Correspondence: Letter from Elmer E. Hazard, Rogers, Hazard & Thames, Attorneys at Law, Jacksonville, Florida, to Dr. and Mrs. Thomas H.B. Walker, Jacksonville, Florida, regarding money due on mortgag

Holland, Rogers & Hazard- Mrs. Rosie Holmes Walker, February 13, 1932

Correspondence: Letter from Elmer E. Hazard, Holland Rogers & Hazard Attorneys at Law, Jacksonville, Florida, to Rosa G. Holmes Walker, Jacksonville, Florida, regarding money due on State and County tax sales certificates for property: North half Lot 5, Block 1, Burbridge\u27s Addition to Jacksonville

Holland, Rogers & Hazard- Mrs. Rosie Holmes Walker, October 30, 1931

Correspondence: Letter from Elmer E. Hazard, Holland Rogers & Hazard Attorneys at Law, Jacksonville, Florida, to Rosa G. Holmes Walker, Jacksonville, Florida, regarding money due on State and County tax sales certificates for property: North half Lot 5, Block 1, Burbridge\u27s Addition to Jacksonville