Automorphisms of Toeplitz B-free systems

• Autorzy: Dymek A.

Identyfikatory

DOI

10.4064/ba8115-10-2017

• Języki publikacji: EN

Abstrakty

EN

For each B-free subshift given by B={2ⁱb_i} i ∈ N, where {b_i} i ∈ N is a set of pairwise coprime odd numbers greater than one, it is shown that the automorphism group of the subshift consists solely of powers of the shift.

Słowa kluczowe

EN

B-free subshift; Toeplitz subshift; automorphism group

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2017
• Tom: Vol. 65, no. 2
• Strony: 139--152
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Dymek A.

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Bibliografia

• [1] E. H. El Abdalaoui, M. Lemańczyk and T. de la Rue, A dynamical point of view on the set of B-free integers, Int. Math. Res. Notices 2015, no. 16, 7258-7286.
• [2] M. Baake and C. Huck, Ergodic properties of visible lattice points, Proc. Steklov Inst. Math. 288 (2015), 165-188.
• [3] A. Bartnicka, S. Kasjan, J. Kułaga-Przymus and M. Lemańczyk, B-free systems revisited, Trans. Amer. Math. Soc., to appear.
• [4] W. Bułatek and J. Kwiatkowski, The topological centralizers of Toeplitz flows and their Z2-extensions, Publ. Mat. 34 (1990), 45-65.
• [5] F. Cellarosi and Ya. G. Sinai, Ergodic properties of square-free numbers, J. Eur. Math. Soc. 15 (2013), 1343-1374.
• [6] V. Cyr and B. Kra, The automorphism group of a minimal shift of stretched exponential growth, J. Modern Dynam. 10 (2016), 483-495.
• [7] H. Davenport and P. Erdos, On sequences of positive integers, Acta Arith. 2 (1936), 147-151.
• [8] H. Davenport and P. Erdos, On sequences of positive integers, J. Indian Math. Soc. (N.S.) 15 (1951), 19-24.
• [9] S. Donoso, F. Durand, A. Maass and S. Petite, On automorphism groups of low complexity subshifts, Ergodic Theory Dynam. Systems 36 (2016), 64-95.
• [10] S. Donoso, F. Durand, A. Maass and S. Petite, On automorphism groups of Toeplitz subshifts, arXiv:1701.00999 (2017).
• [11] T. Downarowicz, Survey of odometers and Toeplitz flows, in: Algebraic and Topological Dynamics, Contemp. Math. 385, Amer. Math. Soc., Providence, RI, 2005, 7-37.
• [12] E. Glasner, Ergodic Theory via Joinings, Math. Surveys Monogr. 101, Amer. Math. Soc., Providence, RI, 2003.
• [13] R. R. Hall, Sets of Multiples, Cambridge Tracts in Math. 118, Cambridge Univ. Press, Cambridge, 1996.
• [14] G. A. Hedlund, Endomorphisms and automorphisms of the shift dynamical system, Math. Systems Theory 3 (1969), 320-375.
• [15] K. Jacobs and M. Keane, 0-1-sequences of Toeplitz type, Z. Wahrsch. Verw. Gebiete 13 (1969), 123-131.
• [16] S. Kasjan, G. Keller and M. Lemańczyk, Dynamics of B-free sets: a view through the window, arXiv:1702.02375 (2017).
• [17] J. Kułaga-Przymus, M. Lemańczyk and B. Weiss, On invariant measures for B-free systems, Proc. London Math. Soc. (3) 110 (2015), 1435-1474.
• [18] M. K. Mentzen, Automorphisms of subshifts defined by B-free sets of integers, Colloq. Math. 147 (2017), 87-94.
• [19] R. Peckner, Uniqueness of the measure of maximal entropy for the squarefree flow, Israel J. Math. 210 (2015), 335-357.
• [20] P. Sarnak, Three lectures on the Möbius function, randomness and dynamics, http://publications.ias.edu/sarnak/.
• [21] S. Williams, Toeplitz minimal flows which are not uniquely ergodic, Z.Wahrsch. Verw. Gebiete 67 (1984), 95-107.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).