Cantor bouquets, explosions, and Knaster continua: dynamic of complex exponentials.
We describe some of the interesting dynamical and topological properties of the complex exponential family λez and its associated Julia sets.
Combinatorics of distance doubling maps
We study the combinatorics of distance doubling maps on the circle ℝ/ℤ with prototypes h(β) = 2β mod 1 and h̅(β) = -2β mod 1, representing the orientation preserving and orientation reversing case, respectively. In particular, we identify parts of the circle where the iterates of a distance doubling map f exhibit “distance doubling behavior”. The results include well known statements for h related to the structure of the Mandelbrot set M. For h̅ they suggest some analogies to the structure of...
Complex a priori bounds revisited