Energy and Invariant Measures for Birational Surface Maps
Complex Variables
2007-05-23 v1 Dynamical Systems
Abstract
When a birational surface map is expanding on cohomology there is a canonical way to associate positive closed currents to the map and its inverse. In this paper we use a version of Dirichlet energy to construct the wedge product of these two currents under a very weak additional condition on the map. We show that the resulting measure is invariant and mixing, and we establish that its Lyapunov exponents are finite and non-zero.
Cite
@article{arxiv.math/0310002,
title = {Energy and Invariant Measures for Birational Surface Maps},
author = {Eric Bedford and Jeffrey Diller},
journal= {arXiv preprint arXiv:math/0310002},
year = {2007}
}
Comments
21 pages