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}
}
  • Wade Hindes, R. Jones
  • Published 2017
  • Mathematics
  • arXiv: Number Theory
  • 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
    Current Trends and Open Problems in Arithmetic Dynamics
    16

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 44 REFERENCES
    Average Zsigmondy sets, dynamical Galois groups, and the Kodaira-Spencer map
    8
    Prime divisors in polynomial orbits over function fields
    4
    Galois representations from pre-image trees: an arboreal survey
    54
    Finitely ramified iterated extensions
    34
    ABC implies primitive prime divisors in arithmetic dynamics
    41
    Primitive divisors in arithmetic dynamics
    43
    Geometric height inequality on varieties with ample cotangent bundles
    12