Dynamics of complex Henon maps: from dynamical space to parameter space

2017 Fiscal Year Final Research Report

• Project/Area Number: 25287020
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kyushu University
• Principal Investigator: Ishii Yutaka 九州大学, 数理学研究院, 准教授 (20304727)
• Co-Investigator(Kenkyū-buntansha): 浅岡 正幸 京都大学, 理学研究科, 准教授 (10314832) ; 荒井 迅 中部大学, 創発学術院, 教授 (80362432)
• Project Period (FY): 2013-04-01 – 2018-03-31
• Keywords: ヘノン写像 / ジュリア集合 / ホースシュー / 反復写像系

Outline of Final Research Achievements

We obtained some results concerning combinatorial and topological aspects of both real and complex Henon maps. Among others, we studied topological properties of the hyperbolic horseshoe locus and the maximal entropy locus in the parameter space of the real Henon family, variational characterization of some invariant measures of the Henon maps at the boundary of the horseshoe locus, and the representation of the monodromy group action of the horseshoe locus for the complex Henon family to the automorphism group of the corresponding symbolic dynamics.

Free Research Field

力学系理論