Geodesic Flows Modelled by Expansive Flows

Given a smooth compact surface without focal points and of higher genus, it is shown that its geodesic flow is semi-conjugate to a continuous expansive flow with a local product structure such that the semi-conjugation preserves time parametrization. It is concluded that the geodesic flow has a unique measure of maximal entropy.

Advanced treatment of biologically pretreated coal gasification wastewater using a novel expansive flow biological intermittent aerated filter process with a ceramic filler from reused coal fly ash

A novel expansive flow biological intermittent aerated filter (BIAF) process was employed for the advanced treatment of real biologically pretreated coal gasification wastewater (CGW) which had poor biodegradability and a low carbon/nitrogen ratio.

Entropy of expansive flows

Let h(φ) be the topological entropy of a real continuous flow φ on a compact metric space X. Introducing an equivalent definition for the topological entropy on an expansive real flow enables us to investigate the topological entropies of mutually conjugate expansive flows and estimate the periodic orbits of an expansive flow which has the pseudo-orbit tracing property.

Real-expansive flows and topological dimension

We examine generalizations of R. Mañé's results on the topological dimension of spaces supporting an expansive homeomorphism to the case of real-expansive flows. We show that a space supporting a real-expansive flow must be finite dimensional, and a minimal real-expansive flow not exhibiting a type of spiral behaviour must be one-dimensional. This latter class includes all known examples and a slight generalization of Axiom A flows. These results are obtained by introducing a new concept of stable and unstable sets for real flows, and examining real-expansive flows in terms of these sets.