On geometrically finite degenerations I: boundaries of main hyperbolic components

  • Yusheng Luo

    Stony Brook University, USA
On geometrically finite degenerations I: boundaries of main hyperbolic components cover

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Abstract

We develop a theory of quasi post-critically finite degenerations of Blaschke products. This gives us tools to study the boundaries of hyperbolic components of rational maps in higher-dimensional moduli spaces. We use it to obtain a combinatorial classification of geometrically finite polynomials on the boundary of the main hyperbolic component , i.e., the hyperbolic component in the space of monic and centered polynomials that contains . We also show that the closure is not a topological manifold with boundary for by constructing self-bumps on its boundary.

Cite this article

Yusheng Luo, On geometrically finite degenerations I: boundaries of main hyperbolic components. J. Eur. Math. Soc. (2023), published online first

DOI 10.4171/JEMS/1342