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Bulletin of the London Mathematical Society Advance Access originally published online on September 19, 2008
Bulletin of the London Mathematical Society 2008 40(6):1017-1024; doi:10.1112/blms/bdn083
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© 2008 London Mathematical Society

Real analyticity of Jacobian of invariant measures for hyperbolic meromorphic functions

Agnieszka Badenska

Faculty of Mathematics and Information Science
Warsaw University of Technology
Pl. Politechniki 1
00-661 Warszawa
Poland

Received 17 July 2007. Revision received 21 May 2008.

We prove that for a hyperbolic meromorphic function f having a rapid derivative growth, if HD (J(f))>1, then the Jacobian Dµ{phi} of a probability invariant measure µ{phi} on J(f), equivalent to a conformal measure m{phi}, has a real analytic extension on a neighbourhood of J(f)\ f–1({infty}) 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.

2000 Mathematics Subject Classification 30D05 (primary), 37F10 (secondary).

The research was supported in part by Warsaw University of Technology Grant No. 504G 1120 0106 000 and by Polish MNiSW Grant ‘Chaos, fraktale i dynamika konforemna’ No. N N201 0222 33.


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