作者：Tardos, G
作者单位：HUN-REN; HUN-REN Institute for Computer Science & Control; Hungarian Academy of Sciences
摘要：The Hanna Neumann conjecture states that the intersection of two nontrivial subgroups of rank k + 1 and I + 1 of a free group has rank at most kl + 1. In a recent paper [3] W. Dicks proved that a strengthened form of this conjecture is equivalent to his amalgamated graph conjecture. He used this equivalence to reprove all known upper bounds on the rank of the intersection. We use his method to improve these bounds. In particular we prove an upper bound of 2kl - k - l + 1 for the rank of the in...
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...
