## EVENT DETAILS AND ABSTRACT

**Dynamical Systems Seminar**
**Title:** Multifractal analysis for multimodal maps

**Speaker:** Professor Mike Todd

**Speaker Info:** University of Porto

**Brief Description:**

**Special Note**:

**Abstract:**

Let $f$ be a multimodal map of the interval $I$. Given an equilibrium state $\mu_\phi$ for a H\"older potential $\phi:I \rightarrow R$, the local dimension $d_{\mu_\phi}(x)$ measures how concentrated $\mu_\phi$ is at this point. The dimension spectrum encodes the Hausdorff dimension of level sets of $d_{\mu_phi}$. This spectrum can be understood via induced maps $(X, F)$, where $F = f^\tau$ for some inducing time $\tau$. A major challenge for maps with critical points is to find inducing schemes which `see' a sufficiently large subset of the space. In this talk I will explain that this problem can be overcome, and hence that, as in the uniformly expanding case, the dimension spectrum is encoded by a function related to the pressure of some potentials involving $\phi$. Many of these results apply not only to Collet-Eckmann maps, but also to maps with much weaker growth conditions.

**Date:** Tuesday, November 04, 2008

**Time:** 3:00pm

**Where:** Lunt 105

**Contact Person:** Prof. Pat Hooper

**Contact email:** wphooper@math.northwestern.edu

**Contact Phone:** 847-491-2853

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