Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Some smooth maps with infinitely many hyperbolic periodic points


Author: John M. Franks
Journal: Trans. Amer. Math. Soc. 226 (1977), 175-179
MSC: Primary 58F20
DOI: https://doi.org/10.1090/S0002-9947-1977-0436221-3
MathSciNet review: 0436221
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: If a smooth map of the two-disk to itself has only hyperbolic periodic points and has no source or sink whose period is a power of two then it has infinitely many periodic points. This and similar results are proved.


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

  • [1] A. Dold, Fixed point index and fixed point theorem for Euclidean neighborhood retracts, Topology 4 (1965), 1-8. MR 33 # 1850. MR 0193634 (33:1850)
  • [2] J. Franks, Morse inequalities for zeta functions, Ann. of Math. (2) 102 (1975), 143-157. MR 0385929 (52:6788)
  • [3] -, A reduced zeta function for diffeomorphisms, Amer. J. Math. (to appear). MR 0494304 (58:13204)
  • [4] M. Shub, Endomorphisms of compact differentiable manifolds, Amer. J. Math. 91 (1969), 175-199. MR 39 #2169. MR 0240824 (39:2169)
  • [5] S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817. MR 37 #3598; erratum, 39, p. 1593. MR 0228014 (37:3598)
  • [6] A. N. Sharkovskiy, Ukrain. Math. J. 16 (1964), 61-71.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58F20

Retrieve articles in all journals with MSC: 58F20


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0436221-3
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society