2008/05/25 by Diller, Jeffrey, Dujardin, Romain, Guedj, Vincent
#32H50 #32U15 #37F10 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.0805.3842
We continue our study of the dynamics of meromorphic mappings with small topological degree 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 admits 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. 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.