Periodic points for birational mappings of P-2

Authors
Citation
C. Favre, Periodic points for birational mappings of P-2, ANN I FOUR, 48(4), 1998, pp. 999
Citations number
11
Categorie Soggetti
Mathematics
Journal title
ANNALES DE L INSTITUT FOURIER
ISSN journal
03730956 → ACNP
Volume
48
Issue
4
Year of publication
1998
Database
ISI
SICI code
0373-0956(1998)48:4<999:PPFBMO>2.0.ZU;2-8
Abstract
We give a sufficient condition for the existence of periodic points for bir ational mappings of CP2. Under this assumption, we get a precise estimation of the number of periodic points with a given period. We give an applicati on of this result to the study of the dynamics of these mappings, by comput ing explicitly the self-intersection of their associated natural invariant current. Our results essentially rely on Bezout's theorem on intersection o f hypersurfaces in the complex projective space, and on the precise study o f intersection multiplicities.