×

zbMATH — the first resource for mathematics

Attractors of transformations of a closed interval. (Russian) Zbl 0653.58022
A piecewise-monotonic smooth mapping f of the interval [0,1] is considered. Let \(f^ n\) denote the n-th iterate of f and use \(\omega\) (x) for the limit set of the trajectory \(\{f^ nx\}^{\infty}_{n=0}\). The typical properties of the dynamical system thus obtained relative to the Lebesgue measure is studied. In earlier works this problem was studied only in the case of unimodel mappings, i.e., mappings that have exactly one critical point.
Reviewer: F.Ling

MSC:
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
PDF BibTeX XML Cite