Equilibrium measures for uniformly quasiregular dynamics
Okuyama, Y., & Pankka, P. (2014). Equilibrium measures for uniformly quasiregular dynamics. London Mathematical Society: Second Series, 89, 524-538. https://doi.org/10.1112/jlms/jdt077
Julkaistu sarjassa
London Mathematical Society: Second SeriesPäivämäärä
2014Tekijänoikeudet
© 2014 London Mathematical Society. This is a final draft version of an article whose final and definitive form has been published by London Mathematical Society & OUP. Published in this repository with the kind permission of the publisher.
We establish the existence and fundamental properties of
the equilibrium measure in uniformly quasiregular dynamics. We show
that a uniformly quasiregular endomorphism f of degree at least 2 on a
closed Riemannian manifold admits an equilibrium measure µf , which
is balanced and invariant under f and non-atomic, and whose support
agrees with the Julia set of f. Furthermore we show that f is strongly
mixing with respect to the measure µf . We also characterize the measure
µf using an approximation property by iterated pullbacks of points
under f up to a set of exceptional initial points of Hausdorff dimension
at most n − 1. These dynamical mixing and approximation results
are reminiscent of the Mattila-Rickman equidistribution theorem
for quasiregular mappings. Our methods are based on the existence of
an invariant measurable conformal structure due to Iwaniec and Martin
and the A-harmonic potential theory.
Julkaisija
Oxford University Press; London Mathematical SocietyISSN Hae Julkaisufoorumista
0024-6107Asiasanat
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