ω-Limit sets for triangular mappings

• Autorzy: Victor Jiménez López , Jaroslav Smítal
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37D45: Strange attractors, chaotic dynamics
• 26A18: Iteration
• 37B45: Continua theory in dynamics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2001
• Tom: 167
• Numer: 1
• Strony: 1-15

Daty

wydano

2001

Twórcy

autor

Victor Jiménez López

• Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain

autor

Jaroslav Smítal

• Institute of Mathematics, Silesian University, 746 01 Opava, Czech Republic

Identyfikatory

DOI

10.4064/fm167-1-1