- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:04:50
Commentarii Mathematici Helvetici
Comment. Math. Helv.
CMH
0010-2571
1420-8946
General
10.4171/CMH
http://www.ems-ph.org/doi/10.4171/CMH
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European Mathematical Society Publishing House
Zuerich, Switzerland
© Swiss Mathematical Society
76
2001
4
Invariant measure and Lyapunov exponents for birational maps of P^2
Jeffrey
Diller
University of Notre Dame, NOTRE DAME, UNITED STATES
Holomorphic dynamics, birational maps, Lyapunov exponents, invariant measures
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.
Measure and integration
General
754
780
10.1007/s00014-001-8327-6
http://www.ems-ph.org/doi/10.1007/s00014-001-8327-6