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Zbl 0758.58024
Silverman, Stephen
On maps with dense orbits and the definition of chaos.
(English)
[J] Rocky Mt. J. Math. 22, No.1, 353-375 (1992). ISSN 0035-7596

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.\par 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.
[G.Osipenko (St.Petersburg)]
MSC 2000:
*37D45 Strange attractors, chaotic dynamics
54H20 Topological dynamics
34D30 Structural stability of ODE

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

Citations: Zbl 0713.58035

Cited in: Zbl 1103.37301

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