Friday, July 26

2:00 PM
## IP10

Multifractality:Physical Evidence and Mathematical Background

A concept of multifractality has been recently developed by physicists and applied mathematicians to study models with irregular turbulent behavior associated with strange attractors. There is physical evidence that a wild fractal structure of these attractors forces the dynamics to exhibit chaotic motions.
A multifractal formalism is a modern tool to analyze data that one can collect while observing distributions of chaotic motions. The rigorous mathematical study of multifractality has recently begun and has shaped a new area of research in the interface of the theory of dynamical systems (mostly of hyperbolic type) and dimension theory (in particular, fractal geometry). This study supported a crucial physical observation that strange attractors have self-similar geometric structure and so have the distributions of chaotic motions. The mathematical study has also revealed that the concept of multifractality is robust in the case of low-dimensional dynamics and may not be so in higher dimensions.

The speaker will discuss aspects of these new concepts and techniques.

**Yakov Pesin**

Department of Mathematics

Pennsylvania State University

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*MMD, 5/20/96*