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Symmetric cubic laminations.
- Source :
-
Conformal Geometry & Dynamics . 7/12/2023, Vol. 27, p264-293. 30p. - Publication Year :
- 2023
-
Abstract
- To investigate the degree d connectedness locus, Thurston [ On the geometry and dynamics of iterated rational maps , Complex Dynamics, A K Peters, Wellesley, MA, 2009, pp. 3–137] studied \sigma _d-invariant laminations , where \sigma _d is the d-tupling map on the unit circle, and built a topological model for the space of quadratic polynomials f(z) = z^2 +c. In the spirit of Thurston's work, we consider the space of all cubic symmetric polynomials f_\lambda (z)=z^3+\lambda ^2 z in a series of three articles. In the present paper, the first in the series, we construct a lamination C_sCL together with the induced factor space \mathbb {S}/C_sCL of the unit circle \mathbb {S}. As will be verified in the third paper of the series, \mathbb {S}/C_sCL is a monotone model of the cubic symmetric connectedness locus , i.e. the space of all cubic symmetric polynomials with connected Julia sets. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10884173
- Volume :
- 27
- Database :
- Academic Search Index
- Journal :
- Conformal Geometry & Dynamics
- Publication Type :
- Academic Journal
- Accession number :
- 164869268
- Full Text :
- https://doi.org/10.1090/ecgd/385