This article does not cite any sources. (December 2009) (Learn how and when to remove this template message)
In one-dimensional complex dynamics, the connectedness locus is a subset of the parameter space of rational functions, which consists of those parameters for which the corresponding Julia set is connected.
The connectedness loci of the higher-degree unicritical families,
(where ) are often called 'Multibrot sets'.
For these families, the bifurcation locus is the boundary of the connectedness locus. This is no longer true in settings, such as the full parameter space of cubic polynomials, where there is more than one free critical point. For these families, even maps with disconnected Julia sets may display nontrivial dynamics. Hence here the connectedness locus is generally of less interest.
- Epstein, Adam; Yampolsky, Michael (March 1999). "Geography of the cubic connectedness locus: Intertwining surgery". Annales Scientifiques de l'École Normale Supérieure. 32 (2): 151–185. arXiv:math/9608213. doi:10.1016/S0012-9593(99)80013-5.
|This mathematics-related article is a stub. You can help Wikipedia by expanding it.|