Rotation sets for unimodal maps of the interval

Christopher Cleveland

doi:10.3934/dcds.2003.9.617

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2003, Volume 9, Issue 3: 617-632. Doi: 10.3934/dcds.2003.9.617

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Rotation sets for unimodal maps of the interval

Christopher Cleveland^1,

1.
Department of Mathematics, Indiana University Purdue University - Indianapolis, 402 N. Blackford Street, Indianapolis, IN 46202

Received: September 30, 2001

Revised: October 31, 2002

Published: April 2003

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Abstract

We relate the rotation interval $\rho(f)$ of a unimodal map $f$ of the interval with its kneading invariant $K(f)$. In particular, we show that for any $\mu \in (0,\frac{1}{2})$, there are kneading invariants $\nu_\mu$ and $\nu_{\mu, h o m}$ such that $\rho(f)=[\mu, \frac{1}{2}]$ if and only if $\nu_\mu \preceq K(f) \preceq \nu_{\mu, h o m}$.

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Mathematics Subject Classification: 26A18, 37B10, 37C25, 37C29, 37E05, 37E15, 37E45.

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