Bulletin of the
Korean Mathematical Society BKMS

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 $\bigotimes \phi_i^*L$ is linearly equivalent to $L^{\bigotimes q}$ 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 \cite{Y}. 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, automorphism

MSC numbers: Primary 14G40, 11G50; Secondary 37P30, 14J28