Bulletin of the Korean Mathematical Society (대한수학회보)

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EQUIDISTRIBUTION OF PERIODIC POINTS OF SOME AUTOMORPHISMS ON K3 SURFACES

  • Lee, Chong-Gyu (Department of Mathematics University of Illinois at Chicago)
  • Received : 2010.10.31
  • Published : 2012.03.31
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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.

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References

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  1. HEIGHT ESTIMATES FOR DOMINANT ENDOMORPHISMS ON PROJECTIVE VARIETIES vol.32, pp.1, 2016, https://doi.org/10.7858/eamj.2016.007
  2. The equidistribution of small points for strongly regular pairs of polynomial maps vol.275, pp.3-4, 2013, https://doi.org/10.1007/s00209-013-1169-2