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Realizing symmetries of a shift

Published online by Cambridge University Press:  19 September 2008

J. B. Wagoner
J. B. Wagoner
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720, USA
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Abstract

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All subshifts of finite type are known to appear as basic parts of the non-wandering sets of Smale diffeomorphisms in dimensions three or more. This paper concerns the symmetries of subshifts of finite type; that is, the homeomorphisms of the shift space which commute with the shift. The group of symmetries is known to be very large for aperiodic shifts. For certain (structually stable) Smale diffeomorphisms of the sphere of dimension five or more, we show each symmetry can be extended to a homeomorphism of the sphere commuting with the diffeomorphism on the whole sphere.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Issue 3 , September 1988 , pp. 459 - 481
Copyright
Copyright © Cambridge University Press 1988

References

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