On Devaney's Definition of Chaos

On chaotic and stable behaviour of the von Foerster–Lasota equation in some Orlicz spaces

“…As proved in the paper of Banks et al [1] the sensitive dependence of the dynamical system on initial conditions in the sense of Guckenhaimer appears immediately from its transitivity and density of the set of its periodic points. This is expressed by the following corollary:…”

On Devaney Chaos and Dense Periodic Points: Period 3 and Higher Implies Chaos

“…Banks et al [3] prove that the sensitivity condition is unnecessary; if f : X → X is a transitive continuous map on an infinite compact metric space X that has a dense set of periodic points, then f has sensitive dependence on initial conditions. Assif and Gadbois [1] show that, for general X , neither transitivity nor dense periodicity are implied by the other two conditions.…”

Open and Dense Topological Transitivity of Extensions by Non-Compact Fiber of Hyperbolic Systems: A Review

“…The original definition of topological chaos given by Devaney, in addition to topological transitivity, requires the existence of a dense set of periodic points and the sensitive dependence of initial data for the dynamical system. It was later shown by Banks et al [4] that the sensitivity of the initial data is a consequence of the other two conditions.…”