Combinatorics and topology of straightening maps II: Discontinuity

Details Combinatorics and topology of straightening maps II: Discontinuity Combinatorics and topology of straightening maps II: Discontinuity

2009-03-25

arxiv.org/abs/0903.4289v2

Mathematics

Dynamical Systems

32 pages, 2 figures

Scientific paper

We continue the study of straightening maps for the family of polynomials of degree d>2. The notion of straightening map is originally introduced by Douady and Hubbard to study the self-similarity of the Mandelbrot set. As expected from their example of a cubic-like family with discontinuous straightening map, we prove that the straightening map is discontinuous unless it is of disjoint type (in this case, it is already known that the straightening map is continuous).

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