Markov pairs, quasi Markov functions and inverse limits

2015/06/02 by Iztok Banič, Banič, Iztok, Matevž Črepnjak +1
Computer Science · Mathematics · #Cellular Automata and Applications #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1506.00876

openalex publication_date 2015/06/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We show that two inverse limits of inverse sequences of closed intervals and quasi Markov bonding functions are homeomorphic, if the inverse sequences follow the same pattern. This significantly improves Holte's result about when two inverse limits of inverse sequences with Markov interval maps as bonding functions are homeomorphic. Our result improves Holte's result in several directions: (1) it generalizes finite Markov partitions to Markov pairs of sets that may even be uncountable, (2) it generalizes Markov interval maps I→ I to quasi Markov functions I→ J (so the domains and the codomains of the bonding functions are not necessarily the same interval), (3) we no longer require the bonding functions to be surjective, and (4) we no longer require the bonding functions to be continuous.

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