2022/03/23 by Hiroyuki Inou, Inou, Hiroyuki, Tomoki Kawahira +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2203.12156
openalex publication_date 2022/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The tricorn, the connectedness locus of the anti-holomorphic quadratic family, is known to be non-locally connected. The boundary of every hyperbolic component of odd period contains arcs that are inaccessible from the complement of the tricorn. As the period increases, the decorations become more and more complicated, and it seems natural to think that every hyperbolic component of sufficiently large and odd period is inaccessible. Contrary to this expectation, we show that the tricorn contains infinitely many hyperbolic components that are accessible from the complement.