Strange attractors in saddle-node cycles: Prevalence and globality

• 成果类型: Article
• 署名作者: Diaz, LJ; Rocha, J; Viana, M
• 署名单位: Universidade do Porto; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s002220050068
• 发表日期: 1996
• 页码: 37-74
• 关键词: hyperbolicity; bifurcation; DYNAMICS; Orbits; sinks; MAPS

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 hyperbolic dynamics.