Topologically completely positive entropy and zero-dimensional\n topologically completely positive entropy

2015/08/20 by Ronnie Pavlov, Pavlov, Ronnie
Computer Science · Mathematics · #37B50 #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1508.05064

openalex publication_date 2015/08/20 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

In a previous paper ("A characterization of topologically completely positive\nentropy for shifts of finite type"), the author gave a characterization for\nwhen a \ℤ^d-shift of finite type (SFT) has no nontrivial subshift\nfactors with zero entropy, a property which we here call zero-dimensional\ntopologically completely positive entropy (ZTCPE). In this work, we study the\ndifference between this notion and the more classical topologically completely\npositive entropy (TCPE) of Blanchard. We show that there are one-dimensional\nsubshifts and two-dimensional SFTs which have ZTCPE but not TCPE. In addition,\nwe show that strengthening the hypotheses of the main result of the\naforementioned paper yields a sufficient condition for a \ℤ^d-SFT to\nhave TCPE.\n

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