## Cubic polynomial maps with periodic critical orbit, Part II: Escape regions

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- by Araceli Bonifant, Jan Kiwi and John Milnor PDF
- Conform. Geom. Dyn.
**14**(2010), 68-112 Request permission

Erratum: Conform. Geom. Dyn.

**14**(2010), 190-193.

## Abstract:

The parameter space $\mathcal {S}_p$ for monic centered cubic polynomial maps with a marked critical point of period $p$ is a smooth affine algebraic curve whose genus increases rapidly with $p$. Each $\mathcal {S}_p$ consists of a compact connectedness locus together with finitely many escape regions, each of which is biholomorphic to a punctured disk and is characterized by an essentially unique Puiseux series. This note will describe the topology of $\mathcal {S}_p$, and of its smooth compactification, in terms of these escape regions. In particular, it computes the Euler characteristic. It concludes with a discussion of the real sub-locus of $\mathcal {S}_p$.## References

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## Additional Information

**Araceli Bonifant**- Affiliation: Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881
- MR Author ID: 600241
- Email: bonifant@math.uri.edu
**Jan Kiwi**- Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica, Casilla 306, Correo 22, Santiago de Chile, Chile
- Email: jkiwi@puc.cl
**John Milnor**- Affiliation: Institute for Mathematical Sciences, Stony Brook University, Stony Brook, New York 11794-3660
- MR Author ID: 125060
- Email: jack@math.sunysb.edu
- Received by editor(s): September 3, 2009
- Published electronically: March 9, 2010
- Additional Notes: The first author was partially supported by the Simons Foundation

The second author was supported by Research Network on Low Dimensional Dynamics PBCT/CONICYT, Chile - © Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn.
**14**(2010), 68-112 - MSC (2010): Primary 37F10, 30C10, 30D05
- DOI: https://doi.org/10.1090/S1088-4173-10-00204-3
- MathSciNet review: 2600536