Symplectic partially hyperbolic automorphisms of 6-torus

Abstract

We study topological properties of automorphisms of a 6-dimensional torus T6 generated by integer matrices with simple eigenvalues being symplectic with respect to either the standard symplectic structure in R6 or a nonstandard symplectic structure given by an integer skew-symmetric non-degenerate matrix. Such a symplectic matrix generates a partially hyperbolic automorphism of the torus, if its eigenvalues lie both outside and on the unit circle. We study transitive and decomposable cases possible here and present a classification in both cases.