2012/10/09 by Carlos Gustavo Moreira, Carlos Gustavo Tamm de Araujo Moreira, Moreira, Carlos Gustavo Tamm de Araujo +2
Computer Science · Mathematics · #28A78 #37D05 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.DS #msc:28A78 #msc:37D05
paper · pdf · doi:10.48550/arxiv.1210.2623
55 pages
arxiv created 2012/10/09 · openalex publication_date 2012/10/09 · arxiv updated 2012/10/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The criterion of the recurrent compact set was introduced by Moreira and Yoccoz to prove that stable intersections of regular Cantor sets on the real line are dense in the region where the sum of their Hausdorff dimensions is bigger than 1. We adapt this concept to the context of horseshoes in ambient dimension higher than 2 and prove that horseshoes with upper stable dimension bigger than 1 satisfy, typically and persistently, the adapted criterion of the recurrent compact set. As consequences we show some persistent geometric properties of these horseshoes. In particular, typically and persistently, horseshoes with upper stable dimension bigger than 1 present blenders.