Pacific Journal of Mathematics

The cohomology of expansive ${\bf Z}^d$-actions by automorphisms of compact, abelian groups.

Anatole B. Katok and Klaus Schmidt

Article information

Source
Pacific J. Math., Volume 170, Number 1 (1995), 105-142.

Dates
First available in Project Euclid: 6 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102371111

Mathematical Reviews number (MathSciNet)
MR1359974

Zentralblatt MATH identifier
0866.28015

Subjects
Primary: 22D40: Ergodic theory on groups [See also 28Dxx]
Secondary: 28D15: General groups of measure-preserving transformations

Citation

Katok, Anatole B.; Schmidt, Klaus. The cohomology of expansive ${\bf Z}^d$-actions by automorphisms of compact, abelian groups. Pacific J. Math. 170 (1995), no. 1, 105--142. https://projecteuclid.org/euclid.pjm/1102371111


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References

  • [Spl] A.Katok and R.J. Spatzier, Differentialrigidity ofhyperbolic abelian actions,preprint, 1992.
  • [Sp2] A.Katok and R.J. Spatzier, Invariant measures for higher rank hyperbolicabelian actions, preprint, 1992.
  • [KiSl] B. Kitchens andK. Sschmit, Automorphisms of compact groups, Ergod. Th. & Dynam. Sys.,9 (1989), 691-735.
  • [KiS2] B. Kitchens andK. Sschmit, Mixing Sets and Relative Entropiesfor Higher Dimensional Markov Shifts, Ergod. Th.k Dynam. Sys.,13 (1993), 705-735.
  • [La] S. Lang, Algebra(2nd Ed.), Addison-Wesley, Reading, Mass.,1984.
  • [iSW] D.Lind, K. Schmidt, andT. Ward, Mahler measure andentropy for commuting automorphisms of compactgroups,Invent. Math., 101(1990), 593-629.
  • [Liv] A. Livshitz, Cohomology of dynamical systems, Math. U.S.S.R. Izvestija, 6 (1972), 1278-1301.
  • [P] K.R. Parthasarathy, Probabilitymeasures on metric spaces,Academic Press, New- York, 1967.
  • [SI] K. Schmidt, Automorphisms of compact abeliangroups andaffine varieties, Proc. London Math. Soc, 61 (1990), 480-496.
  • [S2] K. Schmidt, The cohomology ofhigher-dimensional shifts of finite type,Pac. J.ofMath., 170 (1995), 237-270.
  • [V] W. Veech, Periodicpoints and invariant pseudomeasuresfor toralendomorphisms, Ergod. Th. &Dynam. Sys.,6 (1986), 449-473.
  • [W] A.Weil, Basic Number Theory, Springer Verlag, Berlin-Heidelberg-New York, 1974.