1 citations · 1 across the 2 of their papers we have counts for
5 papers
Local dynamics of non-invertible maps near normal surface singularities
William Gignac, Matteo Ruggiero
We study the problem of finding algebraically stable models for non-invertible holomorphic fixed point germs , where is a complex surface having $x_…
On the growth of local intersection multiplicities in holomorphic dynamics: a conjecture of Arnold
William Gignac
We show by explicit example that local intersection multiplicities in holomorphic dynamical systems can grow arbitrarily fast, answering a question of V. I. Arnold. On the other ha…
Growth of attraction rates for iterates of a superattracting germ in dimension two
William Gignac, Matteo Ruggiero
We study the sequence of attraction rates of iterates of a dominant superattracting holomorphic fixed point germ f:(C^2,0)->(C^2,0). By using valuative techniques similar to those…
Equidistribution of preimages over nonarchimedean fields for maps of good reduction
William Gignac
In this article we prove an analogue of the equidistribution of preimages theorem from complex dynamics for maps of good reduction over nonarchimedean fields. While in general our…
Measures and dynamics on Noetherian spaces
William Gignac
We give an explicit description of all finite Borel measures on Noetherian topological spaces X, and characterize them as objects dual to a space of functions on X. We use these re…