Equivariant Linearization and Rotation Domains on K3 Surfaces

We construct a lot of K3 surface automorphisms of positive entropy having rotation domains of ranks 1 and 2. To carry out this construction, we first lay theoretical foundations concerning equivariant linearization of nonlinear maps under resolutions of quotient singularities, linear models near exceptional components, Salem numbers and multipliers at periodic points, two kinds of fixed point formulas and related indices at exceptional components. Then these basic tools are combined with the method of hypergeometric groups to enable us to detect various types of rotation domains on K3 surfaces.