Chaos-related properties on the product of semiflows

Abstract

In this paper we generalize some results about the chaos-related properties on the product of two semiflows, which appeared in the literature in the last few years, to the case of the most general possible acting monoids. In order to do that we introduce some new notions, namely the notions of a directional, psp and sip monoid, and the notion of a strongly transitive semiflow. In particular, we obtain a sufficient condition for the Devaney chaoticity of a product, which works for the (very large) class of the psp acting monoids.

A note about various types of sensitivity in general semiflows

“…The condition (sp) was introduced in our paper [7], where we discussed chaos-related properties on the product of semiflows. The property (dsp) is for the first time considered in this paper.…”

A note on the sensitivity of semiflows

“…Recently, Miller and Money [11] proved that a non-minimal syndetically transitive semiflow is syndetically sensitive, generalizing some results in [1,3,14,16]. Then, they [12] generalized some results on chaotic properties of cascades to the product of semiflows and asked the following question. (For more recent results on sensitivity, refer to [2,4,5,7,8,9,10,17,18,19,21,22] and some references therein.)…”