Accessible hyperbolic components in anti-holomorphic dynamics

Abstract

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.