The Core Ingram Conjecture for non-recurrent critical points

2015/12/22 by Ana Anusic, Anusic, Ana, Henk Bruin +3
Mathematics · #37B45 #37E05 #54H20 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37B45 #msc:37E05 #msc:54H20

paper · pdf · doi:10.48550/arxiv.1512.07073

arxiv created 2015/12/22 · arxiv updated 2015/12/23

Abstract

We study inverse limit spaces of tent maps, and the Ingram Conjecture, which states that the inverse limit spaces of tent maps with different slopes are non-homeomorphic. When the tent map is restricted to its core, so there is no ray compactifying on the inverse limit space, this result is referred to as the Core Ingram Conjecture. We prove the Core Ingram Conjecture when the critical point is non-recurrent and not preperiodic.

Related

• Accessible points of planar embeddings of tent inverse limit spaces
• Typical path components in tent map inverse limits
• Limit sets of Weil-Petersson geodesics with nonminimal ending\n laminations
• Countable inverse limits of postcritical ω-limit sets of unimodal maps
• Expansivity properties and rigidity for non-recurrent exponential maps