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On maps with dense orbits and the definition of chaos. (English) Zbl 0758.58024
The article deals with a chaotic behaviour in dynamical systems. The object is to examine the relationship between the axioms for the most popular definitions of chaos in discrete systems. The focus is on a definitive analysis in the case of one-dimensional manifold. The dynamical systems are considered on the interval, on the Cantor set, on the circle. It must be noticed the paper “On the definition of chaos” [Z. Angew. Math. Mech. 69, 175-185 (1989; Zbl 0713.58035)] by {\it U. Kirchgraber} and {\it D. Stoffer}, where the same problem is discussed in some other sense.

##### MSC:
 37D45 Strange attractors, chaotic dynamics 54H20 Topological dynamics 34D30 Structural stability of ODE and analogous concepts
Full Text:
##### References:
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