On maps with dense orbits and the definition of chaos. (English) Zbl 0758.58024

Silverman, Stephen

Rocky Mt. J. Math. 22, No. 1, 353-375 (1992).

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.

Reviewer: G.Osipenko (St.Petersburg)

MSC:

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

Keywords:

dense orbit; periodic points; topologically transitive; chaotic behaviour; dynamical systems; discrete systems

Citations:

Zbl 0713.58035

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