Regularity of Dynamical Green Functions

Details Regularity of Dynamical Green Functions Regularity of Dynamical Green Functions

Publishing date

2006-01-10

URL

arxiv.org/abs/math/0601216v2

Science

Mathematics

Field

Complex Variables

Additional info

24 pages, to appear in Transactions of the American Math Society

Type

Scientific paper

Abstract

For meromorphic maps of complex manifolds, ergodic theory and pluripotential theory are closely related. In nice enough situations, dynamically defined Green's functions give rise to invariant currents which intersect to yield measures of maximal entropy. `Nice enough' is often a condition on the regularity of the Green's function. In this paper we look at a variety of regularity properties that have been considered for dynamical Green's functions. We simplify and extend some known results and prove several others which are entirely new. We also give some examples indicating the limits of what one can hope to achieve in complex dynamics by relying solely on the regularity of a dynamical Green's function.

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