Abstract
An automorphism of a subshift of finite type is a homeomorphism of the sub-shift of finite type to itself that commutes with the shift. The automorphisms of a subshift of finite type form a group under composition. In this chapter we study the structure of an automorphism group considered as an abstract group and examine how it acts in the space.
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References
J. Ashley, Marker Automorphisms of the One-sided d-shift, Ergodic Theory and Dynamical Systems 10 (1990), 247–262.
M. Boyle and U.-R. Fiebig, The Action of Inert Finite Order Automorphisms on Finite Subsystems of the Shift, Ergodic Theory and Dynamical Systems 11 (1991), 413–425.
M. Boyle, J. Franks and B. Kitchens, Automorphisms of One-sided Subshifts of Finite Type, Ergodic Theory and Dynamical Systems 10 (1990), 421–449.
P. Blanchard, R. Devaney and L. Keen, The Dynamics of Complex Polynomials, Inventiones Mathematicae 104 (1991), 545–580.
M. Boyle and W. Krieger, Periodic Points and Automorphisms of the Shift, Transactions of the American Mathematical Society 302 (1987), 125–149.
M. Boyle and W. Krieger, Automorphisms and Subsystems of the Shift, Journal für die reine und angewandte Mathematik 437 (1993), 13–28.
M. Boyle, D. Lind and B. Rudolph, The Automorphism Group of a Shift of Finite Type, Transactions of the American Mathematical Society 306 (1988), 71–114.
M. Hall, Jr., The Theory of Groups, Chelsea Publishing Co., 1976.
G.A. Hedlund, Transformations Commuting with the Shift, Topological Dynamics (J. Auslander and W. Gottschalk, eds.), W.A. Benjamin, 1968.
G.A. Hedlund, Endomorphisms and Automorphisms of the Shift Dynamical System, Mathematical Systems Theory 3 no. 4(1969), 320–375.
K.H. Kim and F. Roush, On the Automorphism Groups of Subshifts, PU.M.A Series B 1 (1990), 203–230.
K.H. Kim and F. Roush, On the Structure of Inert Automorphisms of Subshifts, PU.M.A Series B 2 (1991), 3–22.
K.H. Kim, F. Roush and J. Wagoner, Inert Actions on Periodic Points, preprint.
W. Magnus, A. Karrass and D. Solitar. Combinatorial Group Theory, Dover Publications, 1976.
J. Rotman, An Introduction to the Theory of Groups, 3rd. ed., Allyn and Bacon, Inc., 1984.
J.P. Ryan, The Shift and Commutivity, Mathematical Systems Theory 6 (1973), 82–85.
J.P. Ryan, The Shift and Commutivity II, Mathematical Systems Theory 8 (1975), 249–250.
J. Wagoner, Markov Partitions and K 2, Publications Mathematétiques IHES no. 65 (1987), 91–129.
J. Wagoner, Triangle Identities and Symmetries of a Subshift of Finite Type, Pacific Journal of Mathematics 144 (1990), 181–205.
J. Wagoner, Eventual Finite Order Generation for the Kernel of the Dimension Group Representation, Transactions of the American Mathematical Society 317 (1990), 331–350.
R.F. Williams, Classification of Subshifts of Finite Type, Annals of Mathematics 98 (1973), 120–153; Errata 99 (1974), 380-381.
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© 1998 Springer-Verlag Berlin Heidelberg
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Kitchens, B.P. (1998). Automorphisms. In: Symbolic Dynamics. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58822-8_3
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DOI: https://doi.org/10.1007/978-3-642-58822-8_3
Publisher Name: Springer, Berlin, Heidelberg
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