Title: Invariant finite Borel measures for rational functions on the Riemann sphere
Authors: Van Melkebeek, Dieter
Bultheel, Adhemar # ×
Issue Date: 1994
Publisher: Gauthier-Villars
Series Title: Journal de mathématiques pures et appliquées vol:73 issue:2 pages:191-221
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 R-invariant component measures vanishing on the Julia set. The latter one 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.
ISSN: 0021-7824
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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