Transitivity of Surface Dynamics Lifted to Abelian Covers
Dynamical Systems
2008-04-15 v1
Abstract
A homeomorphism f of a manifold M is called H_1-transitive if there is a transitive lift of an iterate of f to the universal Abelian cover \tM. Roughly speaking, this means that f has orbits which repeatedly and densely explore all elements of H_1(M). For a rel pseudo-Anosov map \phi of a compact surface M we show that the following are equivalent: (a) \phi is H_1-transitive, (b) the action of \phi on H_1(M) has spectral radius one, and (c) the lifts of the invariant foliations of \phi to \tM have dense leaves. The proof relies on a characterization of transitivity for twisted \Z^d-extensions of a transitive subshift of finite type.
Cite
@article{arxiv.0804.2245,
title = {Transitivity of Surface Dynamics Lifted to Abelian Covers},
author = {Philip Boyland},
journal= {arXiv preprint arXiv:0804.2245},
year = {2008}
}