Speaker : Zin Arai (Tokyo Institute of Technology)
Title : The Conley index and the topological dimension of hyperbolic Julia sets
Time : 2023-06-06 (Tue) 15:00 - 16:30
Place : Seminar Room 617, Institute of Mathematics (NTU Campus)
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.