Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On fixed points of dynamical systems

Author: Cem Tezer
Journal: Proc. Amer. Math. Soc. 110 (1990), 263-268
MSC: Primary 58F15; Secondary 54H20, 58F20
MathSciNet review: 1013984
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Two fixed points of a topological dynamical system are said to be of the same type if there exists a homeomorphic conjugacy of the system into itself sending the one fixed point into the other. The system will be said to be homogeneous if all its fixed points are of the same type. We introduce algebraic methods to investigate related questions for the shifts of expanding maps.

References [Enhancements On Off] (What's this?)

  • [1] M. Artin and B. Mazur, On periodic points, Ann. of Math. 81 (1965), 82-99. MR 0176482 (31:754)
  • [2] R. F. Brown, The Leftschetz fixed point theorem, Scott, Foresman and Co., Chicago, Illinois, 1971. MR 0283793 (44:1023)
  • [3] M. Gromow, Groups of polynomial growth and expanding maps, IHES Publ. Math. 51 (1981), 53-73. MR 623534 (83b:53041)
  • [4] M. Shub, Endomorphisms of compact differenliable manifolds, Amer. J. Math. 91 (1969), 175-199. MR 0240824 (39:2169)
  • [5] C. Tezer, The shift on the inverse limit of a covering projection, Israel J. Math. 59 (1987), 129-149. MR 920078 (89c:54082)
  • [6] R. F. Williams, Classification of subshift of the finite type, Ann. of Math. 98 (1973), 120-153. MR 0331436 (48:9769)
  • [7] -, Classification of $ 1$-dimensional attractors, Proc. Symp. Pure Math. 14 (1970), 341-361.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58F15, 54H20, 58F20

Retrieve articles in all journals with MSC: 58F15, 54H20, 58F20

Additional Information

Keywords: Expanding maps, Reidemeister numbers, zeta functions
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society