arXiv subjects
Yûsuke Okuyama
Publications and source records attributed to Yûsuke Okuyama.
Lyapunov exponents in complex dynamics and potential theory
This paper is superseded by arXiv:1106.3363.
Potential theory and a characterization of polynomials in complex dynamics
We obtain a measure theoretical characterization of polynomials among rational functions on $\mathbb{P}^1$, 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 study transcendental singularities of a Schröder map arising from a rational function $f$, using results from complex dynamics and Nevanlinna theory. These maps are transcendental meromorphic functions of finite order in the complex plane. We show that their transcendental singularities lie over the set where $f$ is not semihyperbolic (unhyperbolic). In addition, if they are direct, then they lie over only attracting periodic points of $f$, and moreover, if $f$ is a polynomial, then both direct and indirect singularities lie over attracting, parabolic and Cremer periodic points of $f$. We also obtain concrete examples of both kinds of transcendental singularities of Schröder maps as well as a new proof of the Pommerenke-Levin-Yoccoz inequality and a new formulation of the Fatou conjecture.
Linearization problem on structurally finite entire functions
We show that if a 1-hyperbolic structurally finite entire function of type $(p,q)$, $p\ge 1$, is linearizable at an irrationally indifferent fixed point, then its multiplier satisfies the Brjuno condition. We also prove the generalized Mañé theorem; if an entire function has only finitely many critical points and asymptotic values, then for every such a non-expanding forward invariant set that is either a Cremer cycle or the boundary of a cycle of Siegel disks, there exists an asymptotic value or a recurrent critical point such that the derived set of its forward orbit contains this invariant set. From it, the concept of $n$-subhyperbolicity naturally arises.