Yûsuke Okuyama

Repelling periodic points and logarithmic equidistribution in non-archimedean dynamics

It is an open problem whether repelling periodic points are dense in the classical Julia set of a non-archimedean rational function of degree more than one. We give a partial positive answer to this question based on a study of a logarithmic equidistribution on the Berkovich projective line over non-archimedean fields.

Potential theory and a characterization of polynomials in complex dynamics

We obtain a measure theoretical characterization of polynomials among rational functions on

Quantitative approximations of the Lyapunov exponent of a rational function over valued fields

\mathbb{P}^1

Equidistribution of rational functions having a superattracting periodic point towards the activity current and the bifurcation current

, which generalizes a theorem of Lopes. Our proof applies both classical and dynamically weighted potential theory.

Singularities of Schröder Maps and Unhyperbolicity of Rational Functions

We establish a quantitative approximation formula of the Lyapunov exponent of a rational function of degree more than one over an algebraically closed field of characteristic

Adelic equidistribution, characterization of equidistribution, and a general equidistribution theorem in non-archimedean dynamics

0

A Mahler-type estimate of weighted Fekete sums on the Berkovich projective line

0 that is complete with respect to a non-trivial and possibly non-archimedean absolute value, in terms of the multipliers of periodic points of the rational function. This quantifies both our former convergence result over general fields and the one-dimensional version of Berteloot–Dupont–Molino’s one over archimedean fields.

Effective divisors on the projective line having small diagonals and small heights and their application to adelic dynamics

We establish an approximation of the activity current