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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 U. Kirchgraber and D. Stoffer, where the same problem is discussed in some other sense.

37D45Strange attractors, chaotic dynamics
54H20Topological dynamics
34D30Structural stability of ODE and analogous concepts