2018/04/02 by Bautista, Serafin, Valdiane Sales, Sales, Valdiane +2
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Polynomial and algebraic computation #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1804.00646
openalex publication_date 2018/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A hyperbolic set on a compact manifold M, satisfies the property: given two of your any points p and q, such that for all positive ε>0, there is a trajectory in the hyperbolic set from a point ε-close to p to a point ε-close to q, then there is a point in M whose α-limit is that of p and whose ω-limit is that of q. Bautista and Morales give a version of this property, for sectional-Anosov flows (vector fields whose maximal invariant set is sectional-hyperbolic), including some conditions; among them that limit the dimension of M to three. In this paper, we prove a generalization of this result, for sectional-hyperbolic sets of codimension one in high dimensions.