# ω-Limit sets for triangular mappings

Victor Jiménez López; Jaroslav Smítal

Fundamenta Mathematicae (2001)

- Volume: 167, Issue: 1, page 1-15
- ISSN: 0016-2736

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topVictor Jiménez López, and Jaroslav Smítal. "ω-Limit sets for triangular mappings." Fundamenta Mathematicae 167.1 (2001): 1-15. <http://eudml.org/doc/282539>.

@article{VictorJiménezLópez2001,

abstract = {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, in addition, a coherence property is needed. We also provide examples of two slightly different non-Peano continua C and D in the square such that C is and D is not an ω-limit set of a triangular map. In view of these examples a characterization of the continua which are ω-limit sets for triangular mappings seems to be difficult.},

author = {Victor Jiménez López, Jaroslav Smítal},

journal = {Fundamenta Mathematicae},

keywords = {triangular map; Peano continuum; limit set},

language = {eng},

number = {1},

pages = {1-15},

title = {ω-Limit sets for triangular mappings},

url = {http://eudml.org/doc/282539},

volume = {167},

year = {2001},

}

TY - JOUR

AU - Victor Jiménez López

AU - Jaroslav Smítal

TI - ω-Limit sets for triangular mappings

JO - Fundamenta Mathematicae

PY - 2001

VL - 167

IS - 1

SP - 1

EP - 15

AB - 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, in addition, a coherence property is needed. We also provide examples of two slightly different non-Peano continua C and D in the square such that C is and D is not an ω-limit set of a triangular map. In view of these examples a characterization of the continua which are ω-limit sets for triangular mappings seems to be difficult.

LA - eng

KW - triangular map; Peano continuum; limit set

UR - http://eudml.org/doc/282539

ER -

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