43 research outputs found
Density of periodic sources in the boundary of a basin of attraction for iteration of holomorphic maps, geometric coding trees technique
We prove that if A is the basin of immediate attraction to a periodic
attracting or parabolic point for a rational map f on the Riemann sphere, then
periodic points in the boundary of A are dense in this boundary. To prove this
in the non simply- connected or parabolic situations we prove a more abstract,
geometric coding trees version
Dimension properties of the boundaries of exponential basins
We prove that the boundary of a component of the basin of an attracting
periodic cycle (of period greater than 1) for an exponential map on the complex
plane has Hausdorff dimension greater than 1 and less than 2. Moreover, the set
of points in the boundary of which do not escape to infinity has Hausdorff
dimension (in fact: hyperbolic dimension) greater than 1, while the set of
points in the boundary of which escape to infinity has Hausdorff dimension
1.Comment: 13 pages, 1 figur