Errata for “Cubic polynomial maps with periodic critical orbit, Part II: Escape regions”

Bonifant, Araceli; Kiwi, Jan; Milnor, John

doi:10.1090/S1088-4173-2010-00213-4

Errata for “Cubic polynomial maps with periodic critical orbit, Part II: Escape regions”
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by Araceli Bonifant, Jan Kiwi and John Milnor

Conform. Geom. Dyn. 14 (2010), 190-193

DOI: https://doi.org/10.1090/S1088-4173-2010-00213-4

Published electronically: July 26, 2010

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Original Article: Conform. Geom. Dyn. 14 (2010), 68-112.

Abstract:

In this note we fill in some essential details which were missing from our paper. In the case of an escape region $\mathcal {E}_h$ with non-trivial kneading sequence, we prove that the canonical parameter $t$ can be expressed as a holomorphic function of the local parameter $\eta =a^{-1/\mu }$ (where $a$ is the periodic critical point). Furthermore, we prove that for any escape region $\mathcal {E}_h$ of grid period $n\ge 2$, the winding number $\nu$ of $\mathcal {E}_h$ over the $t$-plane is greater or equal than the multiplicity $\mu$ of $\mathcal {E}_h$.

References

A. Bonifant, J. Kiwi and J. Milnor, Cubic Polynomial Maps with Periodic Critical Orbit, Part II: Escape Regions, Conformal Geometry and Dynamics 14 (2010) 68–112.