Geometric Thermodynamical Formalism and Real Analyticity for Meromorphic Functions of Finite Order
نویسندگان
چکیده
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 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.
منابع مشابه
Thermodynamical Formalism and Multifractal Analysis for Meromorphic Functions of finite order
The thermodynamical formalism has been developed in [MyU2] for a very general class of transcendental meromorphic functions. A function f : C → Ĉ of this class is called dynamically (semi-) regular. The key point in [MyU2] was that one worked with a well chosen Riemannian metric space (Ĉ, σ) and that the Nevanlinna theory was employed. In the present manuscript we first improve [MyU2] in provid...
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