American Institute of Mathematical Sciences

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May  2003, 9(3): 617-632. doi: 10.3934/dcds.2003.9.617

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, United States

Received  October 2001 Revised  November 2002 Published  February 2003

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 $\nu_\mu \preceq K(f) \preceq \nu_{\mu, h o m}$.
Keywords: twist itinerary, twist homoclinic itinerary., pattern, Unimodal map, kneading invariant, rotation interval.
Mathematics Subject Classification: 26A18, 37B10, 37C25, 37C29, 37E05, 37E15, 37E4.
Citation: Christopher Cleveland. Rotation sets for unimodal maps of the interval. Discrete & Continuous Dynamical Systems, 2003, 9 (3) : 617-632. doi: 10.3934/dcds.2003.9.617
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