We prove a conjecture of Il'yashenko, that for a C 1 map in R n which locally contracts k-dimensional volumes, the box dimension of any compact invariant set is less than k. This result was proved independently by Douady and Oesterl e and by Il'yashenko for Hausdorr dimension. An upper bound on the box dimension of an attractor is valuable because, unlike a bound on the Hausdorr dimension, it i...

We show that, as conjectured by Adrien Douady back in 1972, every complete metric space is homeomorphic (moreover, isometric) to the locus of zeros of an analytic map between two Banach spaces.

Abstract We generalize a combinatorial formula of Douady from the main cardioid to other hyperbolic components H Mandelbrot set, constructing an explicit piecewise linear map which sends set angles external rays landing on real axis.

In 1939 Douady and others reported for the first time dissociated paralysis of the diaphragm. It occurred in two patients during the course of phrenic alcoholization and pneumoperitoneum therapy for pulmonary tuberculosis. Since then no further cases have been found in the literature. The object of this paper is to report another case and to discuss the therapeutic and anatomical significance o...