Dynamics of meromorphic maps with small topological degree I: from cohomology to currents

Details Dynamics of meromorphic maps with small topological degree I: from cohomology to currents Dynamics of meromorphic maps with small topological degree I: from cohomology to currents

2008-03-06

arxiv.org/abs/0803.0955v3

Mathematics

Complex Variables

Final version, to appear in Indiana University Mathematics Journal. Among other changes, discussion of polynomial maps is impr

Scientific paper

We consider the dynamics of a meromorphic map on a compact kahler surface whose topological degree is smaller than its first dynamical degree. The latter quantity is the exponential rate at which its iterates expand the cohomology class of a kahler form. Our goal in this article and its sequels is to carry out a conjectural program for constructing and analyzing a natural measure of maximal entropy for each such map. Here we take the first step, converting information about the linear action of the map on cohomology to invariant currents with special geometric structure. We also give some examples and identify some additional properties of maps on irrational surfaces and of maps whose invariant cohomology classes have vanishing self-intersection.

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