On maps with dense orbits and the definition of chaos.

*(English)*Zbl 0758.58024The 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.

Reviewer: G.Osipenko (St.Petersburg)

##### MSC:

37D45 | Strange attractors, chaotic dynamics |

54H20 | Topological dynamics |

34D30 | Structural stability of ODE and analogous concepts |