Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-10T05:15:51.575Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

REFERENCES

[B]Birman, J. S.. Braids, links, and mapping class groups. Ann. Math. Studies No. 82, Princeton University Press.Google Scholar
[BK]Boyle, M. & Krieger, W.. Periodic points and automorphisms of the shift, Trans. Amer. Math. Soc. 302 (1987), 125–149.CrossRefGoogle Scholar
[BLR]Boyle, M., Lind, D. & Rudolph, D.. The automorphism group of a subshift of finite type, preprint, University of Washington/University of Maryland, 1986.Google Scholar
[F]Franks, J.. Homology & Dynamical Systems CBMS 49. AMS, Providence, R.I.CrossRefGoogle Scholar
[H]Hedlund, G.. Endomorphisms and automorphisms of the shift dynamical system. Math. Systems Theory 3: 4 (1969), 320–375.CrossRefGoogle Scholar
[Hi]Hirsch, M.. Differential Topology GTM 33, Springer-Verlag, New York 1976.CrossRefGoogle Scholar
[P]Palis, J.. The dynamics of a diffeomorphism and the rigidity of its centralizer. Singularities and Dynamical Systems Pneumatikos, S. N. (ed.), North-Holland, 1985.Google Scholar
[PS]Palis, J. & Smale, S.. Structural stability theorems, Global Analysis, Proc. Symp. Pure Math., AMS XIV (1970), 223–232.CrossRefGoogle Scholar
[R]Robbin, J.. A structural stability theorem, Ann. Math. 94 (1971), 447–493.CrossRefGoogle Scholar
[Ro]Robinson, C.. Structural stability for C1 diffeomorphisms, J Diff. Eq. 22 (1976), 28–73.CrossRefGoogle Scholar
[W]Wagoner, J.. Markov partitions and K2, Pub. Math. I.H.E.S. No. 65 (1987), 91–129.CrossRefGoogle Scholar
[Wi]Williams, R. F.. Classification of subshifts of finite type, Ann. Math. 98 (1973), 120–153;CrossRefGoogle Scholar
Errata 99 (1979), 380–381.CrossRefGoogle Scholar