On the dynamics of dominated splitting

• 成果类型: Article
• 署名作者: Pujals, Enrique R.; Sambarino, Martin
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.169.675
• 发表日期: 2009
• 页码: 675-739
• 关键词: partially hyperbolic systems; homoclinic tangencies; central direction; srb measures; STABILITY

摘要

Let f : M -> M be a C-2-diffeomorphism of a compact surface. We give a complete description of the dynamics of any compact invariant set having dominated splitting. In particular, we prove a Spectral Decomposition Theorem for the limit set L(f) under the assumption of dominated splitting. Moreover, we describe all the bifurcations that these systems can exhibit and the different types of dynamics that could follow for small C-r-perturbations.