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[unknown]

Semyon Dyatlov (0)

Annales de l’institut Fourier

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Sébastien Alvarez, Nicolas Hussenot (0)

Annales de l’institut Fourier

ω-Limit sets for triangular mappings

Victor Jiménez López, Jaroslav Smítal (2001)

Fundamenta Mathematicae

In 1992 Agronsky and Ceder proved that any finite collection of non-degenerate Peano continua in the unit square is an ω-limit set for a continuous map. We improve this result by showing that it is valid, with natural restrictions, for the triangular maps (x,y) ↦ (f(x),g(x,y)) of the square. For example, we show that a non-trivial Peano continuum C ⊂ I² is an orbit-enclosing ω-limit set of a triangular map if and only if it has a projection property. If C is a finite union of Peano continua then,...

Ω-stability for maps with nonwandering critical points

J. Delgado, N. Romero, A. Rovella, F. Vilamajó (2007)

Fundamenta Mathematicae

Sufficient conditions for a map having nonwandering critical points to be Ω-stable are introduced. It is not known if these conditions are necessary, but they are easily verified for all known examples of Ω-stable maps. Their necessity is shown in dimension two. Examples are given of Axiom A maps that have no cycles but are not Ω-stable.

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