Sensitive actions in non-compact spaces
Abstract
Devaney defines a function as chaotic if it satisfies the following three conditions: transitivity, having a dense set of periodic points, and sensitive dependence on initial conditions. In 3, it was demonstrated that the first two conditions imply the third. This result was generalized in aak by replacing the density of periodic points with the density of minimal points. The result was further generalized in g for group actions, in km for C-semigroups actions, and in d for a continuous semi-flow with X being a Polish space. Subsequently, in ip1 and ip2, it was generalized for compact spaces and for non-compact spaces in z. The objective of this work is to generalize the result in z, providing a simple proof.
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