Title: Invariant finite Borel measures for rational functions on the Riemann sphere
Authors: Van Melkebeek, Dieter ×
Bultheel, Adhemar
Issue Date: May-1993
Publisher: Department of Computer Science, K.U.Leuven
Series Title: TW Reports vol:TW191
Abstract: To study finite 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 finite number of mutually singular
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
probability measures on the Riemann sphere in both directions and discuss
how such a measure can be constructed, given a weight function for R.
Publication status: published
KU Leuven publication type: IR
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
× corresponding author

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