Y. Okuyama

activity

20042024

most citedRepelling periodic points and logarithmic equidistribution in non-archimedean dynamics

17 citations · 77 across the 35 of their papers we have counts for

collaborators

35 papers

math.AG2024

Parabolic bifurcation loci in the spaces of rational functions

Yûsuke Okuyama

We give a geometric description of the parabolic bifurcation locus in the space $Rat_{d}$ of all rational functions on $P^{1}$ of degree $d > 1$ , generalizing the…

math.DS2020

Uniform perfectness of the Berkovich Julia sets in non-archimedean dynamics

Yûsuke Okuyama

We show that a rational function $f$ of degree $> 1$ on the projective line over an algebraically closed field that is complete with respect to a non-trivial and non-archimedean abs…

math.NT2020

Resultant measures and minimal resultant loci for non-archimedean polynomial dynamics

Hongming Nie, Yûsuke Okuyama

We compute the resultant measures for iterations $P^{j}$ , $j \geq 1$ , of a polynomial $P$ of degree $> 1$ on the $n$ -th level Trucco's trees $Γ_{n}$ , $n \geq 0$ , in the Berkovich projective…

math.AG2020

On a degenerating limit theorem of DeMarco--Faber

Yûsuke Okuyama

One of our aims is to complement the proof of DeMarco--Faber's degenerating limit theorem for the family of the unique maximal entropy measures parametrized by a punctured open dis…

math.AG2019

Lehto--Virtanen-type and big Picard-type theorems for Berkovich analytic spaces

Yûsuke Okuyama

In non-archimedean setting, we establish a Lehto--Virtanen-type theorem for a morphism from the punctured Berkovich closed unit disk $D ∖ {0}$ in the Be…

math.DS2019

Value distribution of derivatives in polynomial dynamics

Yûsuke Okuyama, Gabriel Vigny

For every $m \in N$ , we establish the equidistribution of the sequence of the averaged pull-backs of a Dirac measure at any given value in $C ∖ {0}$ under t…

math.DS2019★ 1 cited

Entropy in uniformly quasiregular dynamics

Ilmari Kangasniemi, Yûsuke Okuyama, Pekka Pankka +1

Let $M$ be a closed, oriented, and connected Riemannian $n$ -manifold, for $n \geq 2$ , which is not a rational homology sphere. We show that, for a non-constant and non-injective unif…

math.DS2018

A generalization of the converse of Brolin's theorem

Yusuke Okuyama, Malgorzata Stawiska

We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.

math.DS2018★ 2 cited

An a priori bound of rational functions on the Berkovich projective line

Yûsuke Okuyama

We establish a locally uniform a priori bound on the dynamics of a rational function $f$ of degree $> 1$ on the Berkovich projective line over an algebraically closed field of any c…

math.DS2018

Degeneration of quadratic polynomial endomorphisms to a Hénon map

Fabrizio Bianchi, Yûsuke Okuyama

For an algebraic family $(f_{t})$ of regular quadratic polynomial endomorphisms of $C^{2}$ parametrized by $D^{*}$ and degenerating to a Hénon map at $t = 0$ , we study th…

math.DS2018

Approximation of non-archimedean Lyapunov exponents and applications over global fields

Thomas Gauthier, Yusuke Okuyama, Gabriel Vigny

Let $K$ be an algebraically closed field of characteristic 0 that is complete with respect to a non-archimedean absolute value. We establish a locally uniform approximation formula…

math.DS2018

Nevanlinna theory and value distribution in the unicritical polynomials family

Yûsuke Okuyama

In the space $C$ of the parameters $λ$ of the unicritical polynomials family $f (λ, z) = f_{λ} (z) = z^{d} + λ$ of degree $d > 1$ , we establish a quantitative equidistribution result tow…

math.DS2017★ 1 cited

Discontinuity of a degenerating escape rate

Laura DeMarco, Yûsuke Okuyama

We look at degenerating meromorphic families of rational maps on $P^{1}$ -- holomorphically parameterized by a punctured disk -- and we provide examples where the bifurcatio…

math.DS2017★ 2 cited

Hyperbolic components of rational maps: Quantitative equidistribution and counting

Thomas Gauthier, Yûsuke Okuyama, Gabriel Vigny

Let $Λ$ be a quasi-projective variety and assume that, either $Λ$ is a subvariety of the moduli space $M_{d}$ of degree $d$ rational maps, or $Λ$ parametrizes an algebraic…

math.NT2016

Geometric formulas on Rumely's weight function and crucial measure in non-archimedean dynamics

Yûsuke Okuyama

We introduce the $f$ -crucial function $Crucial_{f}$ associated to a rational function $f \in K (z)$ of degree $> 1$ over an algebraically closed field $K$ of possibly pos…

math.NT2016★ 2 cited

Adelically summable normalized weights and adelic equidistribution of effective divisors having small diagonals and small heights on the Berkovich projective lines

Yûsuke Okuyama

We introduce the notion of an adelically summable normalized weight $g$ , which is a family of normalized weights on the Berkovich projective lines satisfying a summability conditio…

math.CV2016

Value distribution of the sequences of the derivatives of iterated polynomials

Yûsuke Okuyama

We establish the equidistribution of the sequence of the averaged pullbacks of a Dirac measure at any value in $C ∖ {0}$ under the derivatives of the iterations of…

math.NT2016

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

Yûsuke Okuyama

We establish a Mahler-type estimate of weighted Fekete sums on the Berkovich projective line over an algebraically closed field of possibly positive characteristic that is complete…

math.NT2015

On a characterization of polynomials among rational functions in non-archimedean dynamics

Yûsuke Okuyama, Małgorzata Stawiska

We study a question on characterizing polynomials among rational functions of degree $> 1$ on the projective line over an algebraically closed field that is complete with respect to…

math.DG2014

A Lehto--Virtanen-type theorem and a rescaling principle for an isolated essential singularity of a holomorphic curve in a complex space

Yûsuke Okuyama

We establish a Lehto--Virtanen-type theorem and a rescaling principle for an isolated essential singularity of a holomorphic curve in a complex space, which are useful for establis…

math.DS2014★ 2 cited

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

Yûsuke Okuyama

We establish an approximation of the activity current $T_{c}$ in the parameter space of a holomorphic family $f$ of rational functions having a marked critical point $c$ by parameter…

math.DG2014★ 1 cited

A generalization of a completeness lemma in minimal surface theory

Yûsuke Okuyama, Katsutoshi Yamanoi

We settle a question posed by Umehara and Yamada, which generalizes a completeness lemma useful in differential geometry.

math.DS2013★ 12 cited

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

Yûsuke Okuyama

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 $0$ t…

math.NT2013★ 4 cited

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

Yûsuke Okuyama

We establish a quantitative adelic equidistribution theorem for a sequence of algebraic zeros divisors on the projective line over the separable closure of a product formula field…