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Energy and Invariant Measures for Birational Surface Maps

Eric Bedford·Jeffrey Diller
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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.

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Eric Bedford, Jeffrey Diller. 2003-09-30. Energy and Invariant Measures for Birational Surface Maps. https://arxiv.org/abs/math/0310002

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