engleski

Topological structure of unimodal inverse limit spaces

Study of inverse limit spaces gained significance in topological dynamics in 1970 when Williams showed that hyperbolic one-dimensional attractors can be represented as inverse limit spaces. We are interested in the topological structure of inverse limit spaces with one tent bonding map. Such inverse limit spaces can be embedded in the plane as global attractors of one-parameter family of planar homeomorphisms and they vary continuously in Hausdorff topology. In 1991 the problem of classifying tent map inverse limits was introduced and became known as the Ingram conjecture. After a sequence of partial results, in 2012, Barge, Bruin and Štimac showed that nondegenerate unimodal inverse limits are all non-homeomorphic. However, the proof crucially depends on the ray compactifying on the core, thus leaving the core version of the conjecture still open. We will discuss the recent results in the case when the critical orbit of the bonding maps is infinite and non-recurrent.

tent map ; inverse limit space ; Ingram conjecture

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