The topological complexity of Cantor attractors for unimodal interval maps

2012/07/12 by Simin Li, Li, Simin, Weixiao Shen +1
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1207.2872

openalex publication_date 2012/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a non-flat C³ unimodal map with a Cantor attractor, we show that for any open cover \mathcal U of this attractor, the complexity function p(\mathcal U, n) is of order nlog n. In the appendix, we construct a non-renormalizable map with a Cantor attractor for which p(U, n) is bounded from above for any open cover U.

Related

• On the algorithmic descriptive complexity of attractors in topological dynamics
• Absorbing Cantor sets in dynamical systems: Fibonacci maps
• On Hausdorff dimension of some Cantor attractors
• Piecewise contracting maps on the interval: Hausdorff dimension, entropy and attractors
• Topological and statistical attractors for interval maps