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Transactions of the American Mathematical Society

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Expansiveness of algebraic actions on connected groups

Author: Siddhartha Bhattacharya
Journal: Trans. Amer. Math. Soc. 356 (2004), 4687-4700
MSC (2000): Primary 37B05; Secondary 54H20
Published electronically: June 22, 2004
MathSciNet review: 2084394
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Abstract: We study endomorphism actions of a discrete semigroup $\Gamma$ on a connected group $G$. We give a necessary and sufficient condition for expansiveness of such actions provided $G$ is either a Lie group or a solenoid.

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  • 1. N. Aoki and M. Dateyama, The relationship between algebraic numbers and expansiveness of automorphisms on compact abelian groups, Fund. Math., no 117, 21-35, 1983. MR 85f:22008
  • 2. S. Bhattacharya, Orbit equivalence and topological conjugacy of affine actions on compact abelian groups, Monatsh. Math., 129, no. 2, 89-96, 2000. MR 2000m:37017
  • 3. M. Boyle and D. Lind, Expansive subdynamics, Trans. Amer. Math. Soc. 349: 55-102, 1997. MR 97d:58115
  • 4. M. Eisenberg, Expansive automorphisms of finite-dimensional vector spaces, Fund. Math., no 59, 307-312, 1966.MR 34:3279
  • 5. N. Jacobson, Lectures in abstract algebra, Vol 2, Van Nostrand, 1953.MR 14:837e
  • 6. A. Katok and K. Schmidt, The cohomology of expansive ${\mathbb Z}^{d}$-actions by automorphisms of compact abelian groups, Pacific J. Math, 170, no. 1, 105-142, 1995. MR 97b:22005
  • 7. B. Kitchens and K. Schmidt, Automorphisms of compact groups, Ergodic Theory and Dynamical Systems 9: 691-735, 1989.MR 91g:22008
  • 8. A. Knapp, Lie groups beyond an introduction, Progress in Mathematics, 140, Birkhäuser, 1996.MR 98b:22002
  • 9. P. F. Lam, On expansive transformation groups, Trans. Amer. Math. Soc. 150: 131-138, 1970. MR 41:7661
  • 10. W. M. Lawton, The structure of compact connected groups which admit an expansive automorphism, Recent advances in Topological Dynamics, Lecture Notes in Mathematics, Springer-Verlag, 1973.MR 52:11873
  • 11. D. Lind and K. Schmidt, Homoclinic points of algebraic ${\mathbb Z}^{d}$-actions, J. Amer. Math. Soc. 12, no. 4, 953-980, 1999.MR 2000d:37002
  • 12. L. S. Pontryagin, Topological groups, Translated from the second Russian edition by Arlen Brown Gordon and Breach Science Publishers, Inc., 1966. MR 34:1439
  • 13. K. Schmidt, Automorphisms of compact abelian groups and affine varieties, Proc. London Math. Soc. 61: 480-496, 1990.MR 91j:28015
  • 14. -, Dynamical systems of algebraic origin, Progress in Mathematics, 128, Birkhäuser Verlag, Basel, 1995.MR 97c:28041

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Additional Information

Siddhartha Bhattacharya
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Mumbai 400005, India

Keywords: Expansive action, Lie group, solenoid
Received by editor(s): September 6, 2000
Received by editor(s) in revised form: April 19, 2001
Published electronically: June 22, 2004
Article copyright: © Copyright 2004 American Mathematical Society

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