In this paper, we develop a theory on the degenerations of Blaschke products d to study the boundaries of hyperbolic components. We give a combinatorial classification of geometrically finite polynomials on the boundary of the main hyperbolic componentd containing zd. We show the closure d⎯⎯⎯⎯⎯⎯⎯⎯ is not a topological manifold with boundary for d≥4 by constructing self-bumps on its boundary.

arXiv:2101.07880