# 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} }

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

#### References

SHOWING 1-10 OF 21 REFERENCES