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The Core Ingram Conjecture for non-recurrent critical orbit

In the early 90's a problem of classifying inverse limits of tent maps with different slopes was posed. It became known as the Ingram conjecture and was finally solved by Barge, Bruin and Štimac in 2012. They showed that nondegenerate inverse limits of tent maps with different slopes are all 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 discuss the partial result of the core version of the Ingram conjecture showing that all cores of inverse limits of tent maps with non-recurrent critical orbit are non-homeomorphic.

tent map ; inverse limit space ; Ingram conjecture

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