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The Core Ingram Conjecture in non-recurrent critical orbit case

In the early 90’s Tom Ingram posed the problem of classifying inverse limit spaces on intervals with the single tent bonding map. These spaces revealed very rich structures and seemed notoriously difficult to classify. Finally, Barge, Bruin and Štimac in 2012. showed that nondegenerate inverse limits of tent maps with different slopes are non-homeomorphic. However, the proof crucially depends on the ray compactifying on the core of the inverse limit space leaving the core version of the conjecture open. We will give a quick overview of the topological properties of these spaces and discuss the recent partial result showing that all cores of inverse limits of tent maps with non-recurrent critical orbits are non-homeomorphic.

tent map ; inverse limit space ; Ingram conjecture

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