Dia: Dimecres, 12 de juliol de 2017
Lloc: Aula S01, Facultat de Matemàtiques i Estadística, UPC.
A càrrec de: Yutaka Ishii, Kyushu University, Japan
Títol: Boundary of the hyperbolic horseshoe locus for the Hénon family
Resum: The purpose of this talk is to investigate geometric and topological properties of the boundary of the parameter locus for the Hénon family where the maps become hyperbolic horseshoes. Our main result states that the boundary of the hyperbolic horseshoe locus forms a piecewise real analytic curve in the parameter space. As a consequence of this result, we show that the hyperbolic horseshoe locus is connected and simply connected, which indicates, in some sense, a weak form of monotonicity. As another consequence, we give a variational characterization of equilibrium measures "at temperature zero" for maps at the boundary parameters. The proofs of these results are based on the the complexification of both the dynamical and the parameter spaces of the Héenon family and employ complex dynamics and complex geometry together with computer assistance. Joint with Zin Arai (Chubu) and Hiroki Takahasi (Keio).
Last updated: Fri Jul 7 10:58:40 2017