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1 June 2005 Energy and invariant measures for birational surface maps
Eric Bedford, Jeffrey Diller
Duke Math. J. 128(2): 331-368 (1 June 2005). DOI: 10.1215/S0012-7094-04-12824-6

Abstract

Given a birational self-map of a compact complex surface, it is useful to find an invariant measure that relates the dynamics of the map to its action on cohomology. Under a very weak hypothesis on the map, we show how to construct such a measure. The main point in the construction is to make sense of the wedge product of two positive, closed (1, 1)-currents. We are able to do this in our case because local potentials for each current have ``finite energy'' with respect to the other. Our methods also suffice to show that the resulting measure is mixing, does not charge curves, and has nonzero Lyapunov exponents.

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Eric Bedford. Jeffrey Diller. "Energy and invariant measures for birational surface maps." Duke Math. J. 128 (2) 331 - 368, 1 June 2005. https://doi.org/10.1215/S0012-7094-04-12824-6

Information

Published: 1 June 2005
First available in Project Euclid: 2 June 2005

zbMATH: 1076.37031
MathSciNet: MR2140266
Digital Object Identifier: 10.1215/S0012-7094-04-12824-6

Subjects:
Primary: 37F10
Secondary: 32H50, 32U40

Rights: Copyright © 2005 Duke University Press

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Vol.128 • No. 2 • 1 June 2005
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