Fractal Measures for Meromorphic Functions of Finite Order
نویسندگان
چکیده
We prove several essential fractal properties, such as positivity, finiteness or local infinity, of Hausdorff and packing measures of radial Julia sets of large subclasses of entire and meromorphic functions considered in [MU]. Most of the results proven are shown to be optimal.
منابع مشابه
Five-value rich lines, Borel directions and uniqueness of meromorphic functions
For a meromorphic function $f$ in the complex plane, we shall introduce the definition of five-value rich line of $f$, and study the uniqueness of meromorphic functions of finite order in an angular domain by involving the five-value rich line and Borel directions. Finally, the relationship between a five-value rich line and a Borel direction is discussed, that is, every Borel direction of $f$ ...
متن کاملGrowth of meromorphic solutions for complex difference equations of Malmquist type
In this paper, we give some necessary conditions for a complex difference equation of Malmquist type $$sum^n_{j=1}f(z+c_j)=frac{P(f(z))}{Q(f(z))},$$ where $n(in{mathbb{N}})geq{2}$, and $P(f(z))$ and $Q(f(z))$ are relatively prime polynomials in $f(z)$ with small functions as coefficients, admitting a meromorphic function of finite order. Moreover, the properties of finite o...
متن کاملSome results on value distribution of the difference operator
In this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. Suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $E_k(1, f^{n}(z)f(z+c))=E_k(1, g^{n}(z)g(z+c))$. Then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(...
متن کاملGeometric Thermodynamical Formalism and Real Analyticity for Meromorphic Functions of Finite Order
Working with well chosen Riemannian metrics and employing Nevanlinna’s theory, we make the thermodynamical formalism work for a wide class of hyperbolic meromorphic functions of finite order (including in particular exponential family, elliptic functions, cosine, tangent and the cosine–root family and also compositions of these functions with arbitrary polynomials). In particular, the existence...
متن کاملOn the Genus of Meromorphic Functions
We define the class of Left Located Divisor (LLD) meromorphic functions and their vertical order m0(f) and their convergence exponent d(f). When m0(f) ≤ d(f) we prove that their Weierstrass genus is minimal. This explains the phenomena that many classical functions have minimal Weierstrass genus, for example Dirichlet series, the Γ-function, and trigonometric functions. 1. LLD meromorphic funct...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005