Geoffrey Hartman

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The Hartman-Grobman Theorem

The Hartman–Grobman Theorem (see [3, page 353]) was proved by Philip Hartman in 1960 [5]. It had been announced byGrobman in 1959 [1], likely unbeknownst to Hartman, and Grobmanpublished his proof in 1962 [2], likely without knowing of Hartman’s work. (Grobman attributes the question to Nemycki and an earlier partial result to R.M. Minc (citing Nauč. Dokl. Vysš. Školy. Fiz.-Mat. Nauki 1 (1958))...

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Let T : x 7→ x + g be an ergodic translation on the compact group C and M ⊆ C a continuity set, i.e. a subset with topological boundary of Haar measure 0. An infinite binary sequence a : Z 7→ {0, 1} defined by a(k) = 1 if T (0C) ∈ M and a(k) = 0 otherwise, is called a Hartman sequence. This paper studies the growth rate of Pa(n), where Pa(n) denotes the number of binary words of length n ∈ N oc...

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ژورنال

عنوان ژورنال: Témoigner. Entre histoire et mémoire

سال: 2014

ISSN: 2031-4183,2506-6390

DOI: 10.4000/temoigner.1488