Attractors of iterated function systems and Markov operators

[摘要] This paper contains a review of results concerning “generalized”attractors for a large class of iterated function systems{wi:i∈I}acting on a complete separable metric space.This generalization, which originates in the Banach contractionprinciple, allows us to consider a new class of sets, which wecall semi-attractors (or semifractals). These sets have manyinteresting properties. Moreover, we give some fixed-pointresults for Markov operators acting on the space of Borelmeasures, and we show some relations between semi-attractors andsupports of invariant measures for such Markov operators.Finally, we also show some relations between multifunctions andtransition functions appearing in the theory of Markov operators.

[学科分类] 数学（综合）