Kavli Affiliate: Zheng Zhu
| First 5 Authors: Jianfei He, Zheng Zhu, , ,
| Summary:
We construct families of rational functions $f: mathbb{P}^1_k rightarrow
mathbb{P}^1_k$ of degree $d geq 2$ over a perfect field $k$ with
non-martingale fixed-point processes. Then for any normal variety $X$ over
$mathbb{P}_{bar{k}}^N$, we give conditions on $f: X rightarrow X$ to
guarantee that the associated fixed-point process is a martingale. This work
extends the previous work of Bridy, Jones, Kelsey, and Lodge on martingale
conditions and answers their question on the existence of a non-martingale
fixed-point process associated with the iterated monodromy group of a rational
function.
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