arXiv subjects

Jernej Cinc

Publications and source records attributed to Jernej Cinc.

3 recordsLinked to original sources

arXiv2019

Accessible points of planar embeddings of tent inverse limit spaces

In this paper we study a class of embeddings of tent inverse limit spaces. We introduce techniques relying on the Milnor-Thurston kneading theory and use them to study sets of accessible points and prime ends of given embeddings. We completely characterize accessible points and prime ends of standard embeddings arising from the Barge-Martin construction of global attractors. In other (non-extendable) embeddings we find phenomena which do not occur in the standard embeddings.

math.DS↗

arXiv2016

Uncountably many planar embeddings of unimodal inverse limit spaces

For point $x$ in the inverse limit space $X$ with a single unimodal bonding map we construct, with the use of symbolic dynamics, a planar embedding such that $x$ is accessible. It follows that there are uncountably many non-equivalent planar embeddings of $X$.

math.DS↗

arXiv2015

The Core Ingram Conjecture for non-recurrent critical points

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.

math.DS↗