Hyperbolic components and cubic polynomials

2017/10/11 by Wang, Xiaoguang · 1 citation
#Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.03955

Abstract

In the space of cubic polynomials, Milnor defined a notable curve \mathcal S_p, consisting of cubic polynomials with a periodic critical point, whose period is exactly p. In this paper, we show that for any integer p≥ 1, any bounded hyperbolic component on S_p is a Jordan disk.

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• Boundary of the central hyperbolic component I: dynamical properties

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