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On ω-limit Sets of Triangular Maps on the Unit Cube
Journal article   Peer reviewed

On ω-limit Sets of Triangular Maps on the Unit Cube

F. Balibrea Gallego, J.L. García Guirao and J.I. Muñoz Casado
Journal of difference equations and applications, Vol.9(3-4), pp.289-304
01/03/2003
DOI: https://doi.org/10.1080/1023619021000047734

Abstract

Discrete Dynamical System Triangular Map Unit Cube ω -Limit Set
In this paper, we construct a triangular map F on I 3 ( I =[0,1]) holding the following uniform property: All points ( a , b , c ) ] I 3 except those of the face I 0 2 ={0} 2 I 2 , which are fixed by F , have as y -limit set the face I 0 2 . So, we are able to describe the family W ( F )={ y F ( a , b , c ):( a , b , c ) ] I 3 } for a continuous endomorphism defined in a compact metric space of dimensión higher than two, establishing that W ( F )= I 0 2 ? {(0, b , c )} ( b , c ) ] I 2 .

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