  Consider a component Q of a stratum in the moduli space of area one abelian
differentials on a surface of genus g. Call a property P for periodic orbits of
the Teichmueller flow typical if the growth rate of orbits with this property
is maximal. Typical are: The logarithms of the eigenvalues of the symplectic
matrix defined by the orbit are arbitrarily close to the Lyapunov exponents of
Q, and its trace field is a totally real splitting field of degree g over Q. If
g>2 then periodic orbits whose SL(2,R)-orbit closure equals Q are typical. We
also show that Q contains only finitely many algebraically primitive
Teichmueller curves, and only finitely many affine invariant submanifolds of
rank at least 2.
