Real analyticity of Jacobian of invariant measures for hyperbolic meromorphic functions | Zendy

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Real analyticity of Jacobian of invariant measures for hyperbolic meromorphic functions

Author(s) -

Badeńska Agnieszka

Publication year - 2008

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/bdn083

Subject(s) - mathematics , meromorphic function , jacobian matrix and determinant , invariant (physics) , bounded function , neighbourhood (mathematics) , analytic function , schwarzian derivative , conformal map , pure mathematics , probability measure , mathematical analysis , mathematical physics

We prove that for a hyperbolic meromorphic function f having a rapid derivative growth, if HD ( J ( f ))>1, then the Jacobian D μ ϕ of a probability invariant measure μ ϕ on J ( f ), equivalent to a conformal measure m ϕ , has a real analytic extension on a neighbourhood of J ( f )∖ f −1 (∞) in ℂ. If, in addition, f satisfies a balanced derivative growth condition with constant exponents, then this extension is bounded in a neighbourhood of every pole of f .

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