** Authors:**
RISONG LI, XIAOLIANG ZHOU

** Abstract: **
In this paper, we mainly discuss how chaos conditions on
semi-flows carry over to their products. We show that if two
semi-flows (or even one of them) are sensitive, so does their product.
On the other side, the product of two topologically transitive
semi-flows need not be topologically transitive. We then provide
several sufficient conditions under which the product of two chaotic
semi-flows is chaotic in the sense of Devaney. Also, stronger forms
of sensitivity and transitivity for product systems are studied. In
particular, we introduce the notion of ergodic sensitivity and prove
that for any given two (not-necessarily continuous) maps
f: X \rightarrow X and g: Y \rightarrow Y (resp. semi-flows \psi:
R^+ \times X \rightarrow X and \phi: R^+ \times Y \rightarrow Y) on
the metric spaces X and Y, f \times g (resp. \psi \times \phi) is
ergodically sensitive if and only if f or g (resp. \psi or \phi) is
ergodically sensitive. Our results improve and extend some existing
ones.

** Keywords: **
Chaos in the sense of Devaney, topological transitivity,
sensitivity

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