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.


37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
54H20 Topological dynamics (MSC2010)
34D30 Structural stability and analogous concepts of solutions to ordinary differential equations


Zbl 0713.58035
Full Text: DOI


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