Fixed-point-free elements of iterated monodromy groups

@article{Jones2012FixedpointfreeEO,
  title={Fixed-point-free elements of iterated monodromy groups},
  author={R. Jones},
  journal={Transactions of the American Mathematical Society},
  year={2012},
  volume={367},
  pages={2023-2049}
}
  • R. Jones
  • Published 2012
  • Mathematics
  • Transactions of the American Mathematical Society
  • The iterated monodromy group of a post-critically finite complex polynomial of degree d \geq 2 acts naturally on the complete d-ary rooted tree T of preimages of a generic point. This group, as well as its pro-finite completion, act on the boundary of T, which is given by extending the branches to their "ends" at infinity. We show that for nearly all polynomials, elements that have fixed points on the boundary are rare, in that they belong to a set of Haar measure zero. The exceptions are those… CONTINUE READING
    9 Citations

    Figures from this paper

    Galois groups and Cantor actions
    • 7
    • Highly Influenced
    • PDF
    Chebyshev action on finite fields
    • 18
    • PDF

    References

    SHOWING 1-10 OF 21 REFERENCES
    Iterated Galois towers, their associated martingales, and the p-adic Mandelbrot set
    • 25
    • PDF
    Laminations in holomorphic dynamics
    • 115
    • PDF
    Iterated Monodromy Groups
    • 12
    The Spectral Problem, Substitutions and Iterated Monodromy
    • 21
    • PDF
    Dynamics in one complex variable
    • 1,361
    Number Theory in Function Fields
    • 654
    ON THERMODYNAMICS OF RATIONAL MAPS. II: NON-RECURRENT MAPS
    • 41
    • PDF
    A note on hyperbolic leaves and wild laminations of rational functions
    • 6
    • PDF