Topological features of flows with the reparametrized gluing orbit property

Abstract

The notions of shadowing, specification and gluing orbit property differ substantially for discrete and continuous time dynamical systems. In the present paper we continue the study of the topological and ergodic properties of continuous flows with the (reparametrized) periodic and nonperiodic gluing orbit properties initiated in [3]. We prove these flows satisfy a weak mixing condition with respect to balls and, if the flow is Komuro expansive, the topological entropy is a lower bound for the exponential growth rate of periodic orbits. Moreover, we show that periodic measures are dense in the set of all invariant probability measures and that ergodic measures are generic. Furthermore, we prove that irrational rotations and some minimal flows on tori and circle extensions over expanding maps satisfy gluing orbit properties, thus emphasizing the difference of this property with respect the notion of specification.