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

  • Jeffrey Diller

    University of Notre Dame, USA
  • Romain Dujardin

    École Polytechnique, Palaiseau, France
  • Vincent Guedj

    Université Paul Sabatier, Toulouse, France
Dynamics of meromorphic mappings with small topological degree II: Energy and invariant measure cover
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Abstract

We continue our study of the dynamics of meromorphic mappings with small topological degree on a compact Kähler surface . 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 has Kodaira dimension zero, or when the mapping is induced by a polynomial endomorphism of . 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.

Cite this article

Jeffrey Diller, Romain Dujardin, Vincent Guedj, Dynamics of meromorphic mappings with small topological degree II: Energy and invariant measure. Comment. Math. Helv. 86 (2011), no. 2, pp. 277–316

DOI 10.4171/CMH/224