Invariant measure and Lyapunov exponents for birational maps of P^2

In this paper we construct and study a natural invariant measure for a birational self-map of the complex projective plane. Our main hypothesis - that the birational map be "separating" - is a condition on the indeterminacy set of the map. We prove that the measure is mixing and that it ha...

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Bibliographic Details
Published in:Commentarii mathematici Helvetici 2001-01, Vol.76 (4), p.754-780, Article 754
Main Author: Diller, Jeffrey
Format: Article
Language:English
Subjects:
Measure and integration
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Summary:In this paper we construct and study a natural invariant measure for a birational self-map of the complex projective plane. Our main hypothesis - that the birational map be "separating" - is a condition on the indeterminacy set of the map. We prove that the measure is mixing and that it has distinct Lyapunov exponents. Under a further hypothesis on the indeterminacy set we show that the measure is hyperbolic in the sense of Pesin theory. In this case, we also prove that saddle periodic points are dense in the support of the measure.
ISSN:0010-2571
1420-8946
DOI:10.1007/s00014-001-8327-6