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The automorphism group of a minimal shift of stretched exponential growth
1. | Department of Mathematics, Bucknell University, 1 Dent Drive, Lewisburg, PA 17837, United States |
2. | Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208, United States |
References:
[1] |
H. Bass, The degree of polynomial growth of finitely generated nilpotent groups, Proc. London Math. Soc. (3), 25 (1972), 603-614. |
[2] |
M. Boyle, D. Lind and D. Rudolph, The automorphism group of a shift of finite type, Trans. Amer. Math. Soc., 306 (1988), 71-114.
doi: 10.1090/S0002-9947-1988-0927684-2. |
[3] |
E. Coven, A. Quas and R. Yassawi, Computing automorphism groups of shifts, using atypical equivalence classes, Discrete Anal., (2016), 1-28.
doi: 10.19086/da.611. |
[4] |
V. Cyr and B. Kra, The automorphism group of a shift of subquadratic growth, Proc. Amer. Math. Soc., 144 (2016), 613-621.
doi: 10.1090/proc12719. |
[5] |
V. Cyr and B. Kra, The automorphism group of a shift of linear growth: beyond transitivity, Forum Math. Sigma, 3 (2015), e5, 27pp.
doi: 10.1017/fms.2015.3. |
[6] |
P. de la Harpe, Topics in Geometric Group Theory, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 2000. |
[7] |
S. Donoso, F. Durand, A. Maass and S. Petite, On automorphism groups of low complexity subshifts, Ergodic Theory Dynam. Systems, 36 (2016), 64-95.
doi: 10.1017/etds.2015.70. |
[8] |
S. Donoso, F. Durand, A. Maass and S. Petite, Private communication. |
[9] |
M. Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math., 53 (1981), 53-73. |
[10] |
Y. Guivarc'h, Groupes de Lie á croissance polynomiale, C. R. Acad. Sci. Paris Sér. A-B, 272 (1971), A1695-A1696. |
[11] |
G. A. Hedlund, Endomorphisms and automorphisms of the shift dynamical system, Math. Systems Theory, 3 (1969), 320-375.
doi: 10.1007/BF01691062. |
[12] |
M. Morse and G. A. Hedlund, Symbolic dynamics II. Sturmian trajectories, Amer. J. Math., 62 (1940), 1-42.
doi: 10.2307/2371431. |
[13] |
K. H. Kim and F. W. Roush, On the automorphism groups of subshifts, Pure Math. Appl. Ser. B, 1 (1990), 203-230. |
[14] |
V. Salo, Toeplitz subshift whose automorphism group is not finitely generated, Colloquium Mathematicum, (2016).
doi: 10.4064/cm6463-2-2016. |
[15] |
V. Salo and I. Törmä, Block maps between primitive uniform and Pisot substitutions, Ergodic Theory and Dynam. Systems, 35 (2015), 2292-2310.
doi: 10.1017/etds.2014.29. |
[16] |
L. van den Dries and A. Wilkie, Gromov's theorem on groups of polynomial growth and elementary logic, J. Algebra, 89 (1984), 349-374.
doi: 10.1016/0021-8693(84)90223-0. |
show all references
References:
[1] |
H. Bass, The degree of polynomial growth of finitely generated nilpotent groups, Proc. London Math. Soc. (3), 25 (1972), 603-614. |
[2] |
M. Boyle, D. Lind and D. Rudolph, The automorphism group of a shift of finite type, Trans. Amer. Math. Soc., 306 (1988), 71-114.
doi: 10.1090/S0002-9947-1988-0927684-2. |
[3] |
E. Coven, A. Quas and R. Yassawi, Computing automorphism groups of shifts, using atypical equivalence classes, Discrete Anal., (2016), 1-28.
doi: 10.19086/da.611. |
[4] |
V. Cyr and B. Kra, The automorphism group of a shift of subquadratic growth, Proc. Amer. Math. Soc., 144 (2016), 613-621.
doi: 10.1090/proc12719. |
[5] |
V. Cyr and B. Kra, The automorphism group of a shift of linear growth: beyond transitivity, Forum Math. Sigma, 3 (2015), e5, 27pp.
doi: 10.1017/fms.2015.3. |
[6] |
P. de la Harpe, Topics in Geometric Group Theory, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 2000. |
[7] |
S. Donoso, F. Durand, A. Maass and S. Petite, On automorphism groups of low complexity subshifts, Ergodic Theory Dynam. Systems, 36 (2016), 64-95.
doi: 10.1017/etds.2015.70. |
[8] |
S. Donoso, F. Durand, A. Maass and S. Petite, Private communication. |
[9] |
M. Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math., 53 (1981), 53-73. |
[10] |
Y. Guivarc'h, Groupes de Lie á croissance polynomiale, C. R. Acad. Sci. Paris Sér. A-B, 272 (1971), A1695-A1696. |
[11] |
G. A. Hedlund, Endomorphisms and automorphisms of the shift dynamical system, Math. Systems Theory, 3 (1969), 320-375.
doi: 10.1007/BF01691062. |
[12] |
M. Morse and G. A. Hedlund, Symbolic dynamics II. Sturmian trajectories, Amer. J. Math., 62 (1940), 1-42.
doi: 10.2307/2371431. |
[13] |
K. H. Kim and F. W. Roush, On the automorphism groups of subshifts, Pure Math. Appl. Ser. B, 1 (1990), 203-230. |
[14] |
V. Salo, Toeplitz subshift whose automorphism group is not finitely generated, Colloquium Mathematicum, (2016).
doi: 10.4064/cm6463-2-2016. |
[15] |
V. Salo and I. Törmä, Block maps between primitive uniform and Pisot substitutions, Ergodic Theory and Dynam. Systems, 35 (2015), 2292-2310.
doi: 10.1017/etds.2014.29. |
[16] |
L. van den Dries and A. Wilkie, Gromov's theorem on groups of polynomial growth and elementary logic, J. Algebra, 89 (1984), 349-374.
doi: 10.1016/0021-8693(84)90223-0. |
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