Speaker: Zin Arai (Institute of Science Tokyo)
Abstract: We study the homological Conley index, a generalization of the Morse index, for the Julia sets of real and complex Hénon maps. A long exact sequence associated with the attractor-repeller decomposition of the filled Julia set is established. As an application, we show that the topological dimension of the Julia set of the Hénon map is one when the map has an attracting periodic orbit and is hyperbolic on the Julia set.
Time: 2025-09-09 16:00:00
Location: R1110, SIMIS
Zoom Meeting ID: 844 0594 7424 (Passcode: 076895)
Introduction to the Speaker: Professor Zin Arai is a researcher at the School of Computing at the Institute of Science Tokyo, working on Dynamical Systems and their applications to Mathematics, Science, and Engineering. He is an expert on the Conley Index, Computer Assisted Proofs, and application to study the dynamics and bifurcations of the Henon map.
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