UCLA

We generalize some properties of surface automorphisms of pseudo-Anosov type.

First, we generalize the Penner construction of a pseudo-Anosov homeomorphism

and show that a symplectic automorphism which is constructed by our generalized

Penner construction has an invariant Lagrangian branched submanifold and an invariant

Lagrangian lamination, which are higher-dimensional generalizations of a

train track and a geodesic lamination in the surface case. Moreover, if a pair consisting

of a symplectic automorphism and a Lagrangian branched surface B satisfies

some assumptions, we prove that there is an invariant Lagrangian lamination L

which is a higher-dimensional generalization of a geodesic lamination.