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- Title
Dynamics of meromorphic mappings with small topological degree II: Energy and invariant measure.
- Authors
Diller, Jeffrey; Dujardin, Romain; Guedj, Vincent
- Abstract
We continue our study of the dynamics of meromorphic mappings with small topological degree λ2(f)<λ1(f) on a compact Kähler surface X. Under general hypotheses we are able to construct a canonical invariant measure which is mixing, does not charge pluripolar sets and has a natural geometric description. Our hypotheses are always satisfied when X has Kodaira dimension zero, or when the mapping is induced by a polynomial endomorphism of C2. They are new even in the birational case (λ2(f)=1). We also exhibit families of mappings where our assumptions are generically satisfied and show that if counterexamples exist, the corresponding measure must give mass to a pluripolar set.
- Subjects
TOPOLOGICAL degree; INVARIANT measures; ENDOMORPHISMS; INTERSECTION numbers; POTENTIAL functions
- Publication
Commentarii Mathematici Helvetici, 2011, Vol 86, Issue 2, p277
- ISSN
0010-2571
- Publication type
Article
- DOI
10.4171/CMH/224