Geography of the cubic connectedness locus: Intertwining surgery

Authors
Epstein, A Yampolsky, M
Citation
A. Epstein et M. Yampolsky, Geography of the cubic connectedness locus: Intertwining surgery, ANN SCI EC, 32(2), 1999, pp. 151-185
Citations number
32
Categorie Soggetti
Mathematics
Journal title
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE
ISSN journal
00129593 → ACNP
Volume
32
Issue
2
Year of publication
1999
Pages
151 - 185
Database
ISI
SICI code
0012-9593(199903/04)32:2<151:GOTCCL>2.0.ZU;2-X
Abstract
We exhibit products of Mandelbrot sets in the two-dimensional complex param eter space of cubic polynomials. Cubic polynomials in such a product may be renormalized to produce a pair of quadratic maps. The inverse construction intertwining two quadratics is realized by means of quasiconformal surgery . The associated asymptotic geography of the cubic connectedness locus is d iscussed in the Appendix. (C) Elsevier, Paris.