Resumen de Dynamics of meromorphic mappings with small topological degree II: Energy and invariant measure

Jeffrey Diller, Romain Dujardin, Vincent Guedj

• We continue our study of the dynamics of meromorphic mappings with small topological degree ?2(f)

  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 (?2(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.