The structure of compact connected groups which admit an expansive automorphism

  • Wayne Lawton
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 318)


Topological Entropy Finite Rank Integer Entry Compact Topological Space Mathematical System Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abramov, L. M., The entropy of an automorphism of a solenoidal group, Theory of Probability and its Applications, vol. 4 (1959), pp. 231–236 (English translation).MathSciNetCrossRefGoogle Scholar
  2. 2.
    Adler, R. M.; Konheim, A. G.; McAndrew M. H., Topological entropy, Transactions of the American Mathematical Society, vol. 114 (1965), pp. 309–319.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Aoki, N., Topological entropy and measure for automorphisms on compact groups, Mathematical Systems Theory, vol. 5, (1971), pp. 4–7.MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Arov, D. Z., Topological similitude of automorphisms and translations of compact commutative groups, Uspehi Mathematiceskih Nauk, vol. 18 (1963), no. 5 pp. 133–138 (Russian).MathSciNetzbMATHGoogle Scholar
  5. 5.
    Artin, M.; Mazur, B., On periodic points, Annals of Mathematics, vol. 81 (1965), pp. 82–99.MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Auslander, J.; Gottschalk, W. H., (editors) Topological dynamics, An international symposium, Benjamin, New York, 1968.zbMATHGoogle Scholar
  7. 7.
    Eisenberg, M., Expansive automorphisms of finite dimensional vector spaces, Fundamenta Mathematicae, vol. 59 (1966), pp. 307–312.MathSciNetzbMATHGoogle Scholar
  8. 8.
    Eisenberg, M., Expansive transformation semi groups of endomorphisms, Fundamenta Mathematicae, vol. 59 (1966), pp. 313–321.MathSciNetzbMATHGoogle Scholar
  9. 9.
    Gottschalk, W. H.; Hedlund, G. A., Topological dynamics, American Mathematical Society Colloquium Publications, vol. 36. American Mathematical Society, Providence, 1955.Google Scholar
  10. 10.
    Hedlund, G. A., Endomorphisms and automorphisms of shift dynamical systems, Mathematical Systems Theory, vol. 3 (1969), pp. 320–375.MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Helgason, S. Differential geometry and symmetric spaces, Academic Press, New York, 1962.zbMATHGoogle Scholar
  12. 12.
    Hewitt, E.; Ross K. A.; Abstract harmonic analysis, vol. 1. Springer Verlag, Berlin; 1963.CrossRefGoogle Scholar
  13. 13.
    Hofmann, K. H.; Mostert, P., Splitting in topological groups, Memoirs of the American Mathematical Society, no. 43. American Mathematical Society, Providence, 1963.Google Scholar
  14. 14.
    Keynes, H. B.; Robertson, J. B., Generators for topological entropy and expansiveness, Mathematical Systems Theory, vol, 3 (1969), pp. 51–59.MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Lam, Ping-Fun, On expansive transformation groups, Transactions of the American Mathematical Society, vol. 150 (1970), pp. 131–138.MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Montgomery, Deane; Zippin, Leo, Topological transformation groups, Interscience Tracts in Pure and Applied Mathematics, Tract 1, Interscience, New York, 1955.Google Scholar
  17. 17.
    Pontryagin, L., Topological groups, Princeton Mathematical Series, vol. 2. Princeton University Press, Princeton, 1939.Google Scholar
  18. 18.
    Reddy, William, The existence of expansive homeomorphisms on manifolds, Duke Mathematical Journal, vol. 32 (1965), pp. 494–509.CrossRefGoogle Scholar
  19. 19.
    Smale, Stephen, Differentiable dynamical systems, Bulletin of the American Mathematical Society, vol. 73 (1967) pp. 747–817.MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Walters, Peter, Introductory lectures on ergodic theory, lecture notes, University of Maryland, College Park, Maryland, 1970.Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Wayne Lawton
    • 1
  1. 1.Wesleyan UniversityUSA

Personalised recommendations