arXiv subjects

Zheng Jian-Hua

Publications and source records attributed to Zheng Jian-Hua.

2 recordsLinked to original sources

arXiv2012

Dynamics of Hyperbolic Meromorphic Functions

A definition of hyperbolic meromorphic functions is given and then we discuss the dynamical behavior and the thermodynamic formalism of hyperbolic functions on the Julia set. We prove the important expanding properties for hyperbolic functions on the complex plane and with respect to the euclidean metric. We establish the Bowen formula for hyperbolic functions on the complex plane, that is, the Poincare exponent equals to the Hausdorff dimension of the radial Julia set and furthermore, we prove that all the results in the Walters' theory hold for hyperbolic functions on the Riemann sphere.

math.CV↗

arXiv2007

Non-existence of unbounded Fatou components of a meromorphic function

This paper is devoted to establish sufficient conditions under which a transcendental meromorphic function has no unbounded Fatou components and to extend some results for entire functions to meromorphic functions. Actually, we shall mainly discuss non-existence of unbounded wandering domains of a meromorphic function. The case for a composition of finitely many meromorphic function with at least one of them being transcendental can be also investigated in the argument of this paper.

math.CV↗