The existence of conformal measures for some transcendental meromorphic functions

2006 ◽  
pp. 169-201 ◽  
Author(s):  
Bartłomiej Skorulski
Keyword(s):  
Meromorphic Functions ◽  
Conformal Measures

Conformal measures for non-entire functions with critical values eventually mapped onto infinity

Analysis ◽  
2005 ◽  
Vol 25 (4) ◽  
Author(s):  
Janina Kotus
Keyword(s):  
Meromorphic Functions ◽  
Fractal Structure ◽  
Entire Functions ◽  
Critical Values ◽  
Conformal Measures

SummaryThis paper is a continuation of our earlier works [7] and [9] on the fractal structure of expanding and subexpanding meromorphic functions of the form

Geometric thermodynamic formalism and real analyticity for meromorphic functions of finite order

2008 ◽  
Vol 28 (3) ◽  
pp. 915-946 ◽  
Author(s):  
VOLKER MAYER ◽  
MARIUSZ URBAŃSKI
Keyword(s):  
Finite Order ◽  
Exponential Family ◽  
Meromorphic Functions ◽  
Julia Set ◽  
Gibbs Measures ◽  
Thermodynamic Formalism ◽  
Riemannian Metrics ◽  
Elliptic Functions ◽  
Real Analyticity ◽  
Conformal Measures

AbstractWorking with well chosen Riemannian metrics and employing Nevanlinna’s theory, we make the thermodynamic 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 of conformal (Gibbs) measures is established and then the existence of probability invariant measures equivalent to conformal measures is proven. As a geometric consequence of the developed thermodynamic formalism, a version of Bowen’s formula expressing the Hausdorff dimension of the radial Julia set as the zero of the pressure function and, moreover, the real analyticity of this dimension, is proved.

Further investigations on Fujimoto type strong uniqueness polynomials

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5203-5216
Author(s):  
Abhijit Banerjee ◽  
Bikash Chakraborty ◽  
Sanjay Mallick
Keyword(s):  
Meromorphic Functions ◽  
Future Research ◽  
Strong Uniqueness ◽  
Open Questions

Taking the question posed by the first author in [1] into background, we further exhaust-ably investigate existing Fujimoto type Strong Uniqueness Polynomial for Meromorphic functions (SUPM). We also introduce a new kind of SUPM named Restricted SUPM and exhibit some results which will give us a new direction to discuss the characteristics of a SUPM. Moreover, throughout the paper, we pose a number of open questions for future research.

On Fixed Points of Meromorphic Functions f(z) and f(z + c), Δcf(z)

2019 ◽  
Vol 39 (5) ◽  
pp. 1277-1289
Author(s):  
Shuangting Lan ◽  
Zongxuan Chen
Keyword(s):  
Fixed Points ◽  
Meromorphic Functions
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