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http://dx.doi.org/10.4134/BKMS.2012.49.2.307

EQUIDISTRIBUTION OF PERIODIC POINTS OF SOME AUTOMORPHISMS ON K3 SURFACES  

Lee, Chong-Gyu (Department of Mathematics University of Illinois at Chicago)
Publication Information
Bulletin of the Korean Mathematical Society / v.49, no.2, 2012 , pp. 307-317 More about this Journal
Abstract
We say (W, {${\phi}_1,\;{\ldots}\;,{\phi}_t$}) is a polarizable dynamical system of several morphisms if ${\phi}_i$ are endomorphisms on a projective variety W such that ${\otimes}{\phi}_i^*L$ is linearly equivalent to $L^{{\otimes}q}$ for some ample line bundle L on W and for some q > t. If q is a rational number, then we have the equidistribution of small points of given dynamical system because of Yuan's work [13]. As its application, we can build a polarizable dynamical system of an automorphism and its inverse on a K3 surface and can show that its periodic points are equidistributed.
Keywords
equidistribution; height; dynamical system; K3 surface; auto-morphism;
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