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arXiv · 0908.3326

On Yoccoz Return Functions

Nathaniel D. Emerson
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Abstract

We study the dynamics of complex polynomials. We obtain results on Poincare return maps defined on certain neighborhoods of a point with bounded orbit under a polynomial. We introduce a generalization of the Yoccoz tau-function, the Yoccoz return function, which codes the returns of a critical point with bounded orbit of any complex polynomial with a disconnect Julia set. We give necessary conditions on Yoccoz return functions, which allow for the recursive definition of an abstract tau-function. These conditions are also sufficient for polynomials that have a disconnected Julia set and exactly one critical point with bounded orbit.

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Nathaniel D. Emerson. 2009-08-23. On Yoccoz Return Functions. https://arxiv.org/abs/0908.3326

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