We extend the unpublished work of M. Handel and R. Miller on the
classification, up to isotopy, of endperiodic automorphisms of surfaces. We
give the Handel-Miller construction of the geodesic laminations, give an
axiomatic theory for pseudo-geodesic lamaniations, show the geodesic
laminations satisfy the axioms, and prove that paeudo-geodesic laminations
satisfying our axioms are ambiently isotopic to the geodesic laminations. The
axiomatic approach allows us to show that the given endperiodic automorphism is
isotopic to a smooth endperiodic automorphism preserving smooth laminations
ambiently isotopic to the original ones. Using the axioms, we also prove the
"transfer theorem" for foliations of 3-manifolds., namely that, if two depth
one foliations are transverse to a common one-dimensional foliation whose
monodromy on the noncompact leaves of the first foliation exhibits the nice
dynamics of Handel-Miller theory, then the transverse one-dimensional foliation
also induces monodromy on the noncompact leaves of the second foliation
exhibiting the same nice dynamics. Our theory also applies to surfaces with
infinitely many ends.Comment: Added Sergio Fenley as author. Moved material from Section 12.6 to a
new Section 6.7. Rewrote Section 7. Deleted material from Section 6.1 and
combined Sections 6.1 and 6.2 into new Section 6.1. Rewrote Section 4.6.
Corrected typos and errors and improved expositio