The Mandelbrot Set is Universal
By Curtis T. McMullen. 2000
105 citations recorded by the source corpus.
We show small Mandelbrot sets are dense in the bifurcation locus for any holomorphic family of rational maps.
Subfields: Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3d31e398c194c76fc6519927f1983da3c6c666cc
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In Computational Theory and Mathematics
- Romain Dujardin
- Christian Henriksen
- Dierk Schleicher
- Xavier Buff
- C. Favre
- Mattias Jonsson
- Chi Li
- Matthew Baker
In Mathematical Physics
- Romain Dujardin
- Christian Henriksen
- Dierk Schleicher
- Xavier Buff
- C. Favre
- Xie Junyi
- Mattias Jonsson
- Franccois Berteloot
Citations in the corpus
- ATTRACTING DYNAMICS OF EXPONENTIAL MAPS (2003, background): “The importance of the study of the space of quadratic polynomials stems not only from the fact that they are the simplest class of rational maps, but also because renormalization theory [DH2] shows that quadratic polynomials have universal properties; as a consequence, every non-trivial bifurcation ”
- Distribution of rational maps with a preperiodic critical point (2006, methodology): “The following result is a little bit more delicate (see also [Le1, McM1 ]).”
- On König's root-finding algorithms* (2003, background): “The existence of such a copy is not surprising: McMullen [ McM3 ] showed that copies of the Mandelbrot set (or generalizations known as multibrot sets) are dense in the bifurcation locus of any analytic family of rational maps.”