Invariant Nite Borel Measures for Rational Functions on the Riemann Sphere
نویسنده
چکیده
To study nite Borel measures on the Riemann sphere invariant under a rational function R of degree greater than one, we decompose them in an R-invariant component measure supported on the Julia set and a nite number of mutually singular R-invariant component measures vanishing on the Julia set. The latter ones can be described easily. For a characterization of the former one, we use a general approach based on a weight function for R on the Riemann sphere. We investigate the relation between weight functions for R and R-invariant Borel probability measures on the Riemann sphere in both directions and discuss how such a measure can be constructed, given a weight function for R.
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