Genadi Levin (Hebrew U.)

will speak on

Dimension of the basin of Feigenbaum's attractors.

Abstract:

In spite of many efforts, the problem of existence of a positive area Julia set is open. We give an overview of this and related problems. A plausible candidate for such "fat" system is Feigenbaum's polynomial $z^d+c_f$, particularly when the order $d$ is high. To this direction, we prove that the Julia set of such polynomial is (asymptotically) "thick", i.e. its Hausdorff dimension tends to $2$ as $d$ grows. Joint work with G. Swiatek.

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Last update on 20/10/02.