Comptes Rendus
Dynamical Systems
A model for the parabolic slices Per1(e2πip/q) in moduli space of quadratic rational maps
Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1327-1330.

The notion of relatedness loci in the parabolic slices Per1(e2πip/q) in moduli space of quadratic rational maps is introduced. They are counterparts of the disconnectedness or escape locus in the slice of quadratic polynomials. A model for these loci is presented, and a strategy of proof of the faithfulness of the model is given.

Nous introduisons la notion de lieux de parenté dans les sections paraboliques Per1(e2πip/q) de l'espace des modules des fractions rationnelles quadratiques. Ce sont des analogues du lieu de non-connexité dans la section correspondant aux polynômes quadratiques. Nous présentons un modèle pour ces lieux, et donnons une stratégie de preuve de la fidélité de ce modèle.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2010.10.033

Eva Uhre 1, 2

1 Institut de mathématiques de Toulouse, Université Paul-Sabatier, 31062 Toulouse cedex, France
2 NSM, Roskilde University, 4000 Roskilde, Denmark
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Eva Uhre. A model for the parabolic slices $ {\mathrm{Per}}_{1}({e}^{2\pi ip/q})$ in moduli space of quadratic rational maps. Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1327-1330. doi : 10.1016/j.crma.2010.10.033. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.10.033/

[1] L.R. Goldberg; L. Keen The mapping class group of a generic quadratic rational map and automorphisms of the 2-shift, Invent. Math., Volume 101 (1990) no. 2, pp. 335-372

[2] J. Milnor, Hyperbolic components in spaces of polynomial maps, IMS Stony Brook, preprint #3(1992).

[3] J. Milnor Geometry and dynamics of quadratic rational maps, Experiment. Math., Volume 2 (1993) no. 1, pp. 37-83

[4] C.L. Petersen No elliptic limits for quadratic maps, Ergod. Th. & Dynam. Sys., Volume 19 (1999), pp. 127-141

[5] C.L. Petersen; L. Tan Analytic coordinates recording cubic dynamics (D. Schleicher, ed.), Complex Dynamics, Families and Friends, A.K. Peters, 2009, pp. 413-450

[6] M. Rees Components of degree two hyperbolic rational maps, Invent. Math., Volume 100 (1990), pp. 357-382

[7] E. Uhre, The structure of parabolic slices Per1(e2πip/q) in moduli space of quadratic rational maps, manuscript, 2009.

[8] B. Wittner, On the bifurcation loci of rational maps of degree two, PhD thesis, Cornell University, 1988.

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