Dynamics on the Riemann Sphere
Full-Text PDF (142 KB) | Book articles | Book details
(2) Stony Brook University, USA
We give examples of infinitely renormalizable quadratic polynomials Fc : z ↦ z2 + c with stationary combinatorics whose Julia sets have Hausdorff dimension arbitrary close to 1. The combinatorics of the renormalization involved is close to the Chebyshev one. The argument is based upon a new tool, a "Recursive Quadratic Estimate" for the Poincaré series of an infinitely renormalizable map.
No keywords available for this article.