# Riccati equations and polynomial dynamics over function fields

@article{Hindes2017RiccatiEA, title={Riccati equations and polynomial dynamics over function fields}, author={Wade Hindes and R. Jones}, journal={arXiv: Number Theory}, year={2017} }

Given a function field $K$ and $\phi \in K[x]$, we study two finiteness questions related to iteration of $\phi$: whether all but finitely many terms of an orbit of $\phi$ must possess a primitive prime divisor, and whether the Galois groups of iterates of $\phi$ must have finite index in their natural overgroup $\text{Aut}(T_d)$, where $T_d$ is the infinite tree of iterated preimages of $0$ under $\phi$. We focus particularly on the case where $K$ has characteristic $p$, where far less is… CONTINUE READING

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