Topological and Combinatorial Problems in One-dimensional Complex Dynamics

GEOMETRY OF CARPETS JULIA SET OF RATIONAL MAPS

speaker: Jinsong ZENG (Université d'Angers)

abstract: Let fbe a rational map whose Julia set J(f) is a Sierpi´ nski carpet. We prove that J(f) is quasisymmetrically equivalent to a round carpet if the w-limit sets of the critical points of fare disjoint with the boundaries of the periodic Fatou components. The peripheral circles of J(f) are uniform quasicircles if the boundaries of periodic Fatou component have no parabolic points and w(c), for any recurrent points. Moreover, if fhas no recurrent critical points, then they satisfy the uniformly relatively separated condition if and only if the accumulation points of the critical orbits are disjoint with the boundary of the strictly pre-periodic Fatou components

timetable:
Wed 16 Oct, 16:45 - 17:15, Aula Dini
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