The parameter capturemap for V_3

Details The parameter capturemap for V_3 The parameter capturemap for V_3

2012-01-19

arxiv.org/abs/1201.4082v1

Mathematics

Dynamical Systems

134 pages

Scientific paper

This is a study of the Wittner capture construction for critically finite quadratic rational maps for which one critical point is periodic, and the second critical point is in the backward orbit of the first. This construction gives a way of describing rational maps up to topological conjugacy. It is known that representations as Wittner captures are not unique. We show that, in a certain parameter space which we call $V_3$, the set of maps with exactly $2^r$ representations as a Wittner capture is of density bounded from 0 for each $r\geq 0$, and for each fixed preperiod of the second critical point.

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