ON THE DYNAMICS OF HOMOLOGY-PRESERVING HOMEOMORPHISMS OF THE ANNULUS

摘要

We consider the homeomorphisms of the compact annulus A = S-1 x [-1, 1] isotopic to the symmetry S-A which interchanges the two boundary components. We prove that if such a homeomorphism is, in some sense, conservative and twisted, then it possesses a periodic orbit of period exactly two. This can be regarded as a counterpart of the Poincare-Birkhoff theorem in the isotopy class of S-A.