作者：He, ZX; Schramm, O
作者单位：Weizmann Institute of Science
摘要：Rodin and Sullivan (1987) proved Thurston's conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby providing a refreshing geometric view of Riemann's Mapping Theorem. We now present a new proof of the Rodin-Sullivan theorem. This proof is based on the argument principle, and has the following virtues. 1. It applies to more general packings. The Rodin-Sullivan paper deals with packings based on the hexagonal combinatorics. Later, quantitative esti...
作者：Diaz, LJ; Rocha, J; Viana, M
作者单位：Universidade do Porto; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We consider parametrized families of diffeomorphisms bifurcating through the creation of critical saddle-node cycles. We show that they always exhibit Henon-like strange attractors for a set of parameter values with positive Lebesgue density at the bifurcation value. Zn open classes of such families the strange attractors are of global type: their basins contain an a priori defined neighbourhood of the cycle. Furthermore, the bifurcation parameter may also be a point of positive density of hyp...
