Surfaces of section for expansive flows on three-manifolds

摘要

A continuous non singular flow φ_t: X→X on the metric space X is said to be expansive if any ε > 0 exist δ > 0 such that if x, y∈=X satisfy d(φ_t(x), φ_(h(t))(y))<δ anyt∈R for some continuous function h: R→R, h(0)=0, then y=φ_s(x) for some s∈:(—ε, ε) (see , where there are some other equivalent definitions). A classical example of expansive flow is given by an Anosov flow; another example is the suspension of a pseudo-Anosov diffeomorphism.