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)

 
 

 

Orientation-reversing Morse-Smale diffeomorphisms on the torus


Author: Steve Batterson
Journal: Trans. Amer. Math. Soc. 264 (1981), 29-37
MSC: Primary 58F09
DOI: https://doi.org/10.1090/S0002-9947-1981-0597864-0
MathSciNet review: 597864
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For orientation-reversing diffeomorphisms on the torus necessary and sufficient conditions are given for an isotopy class to admit a Morse-Smale diffeomorphism with a specified periodic behavior.


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

  • [B] S. Batterson, The dynamics of Morse-Smale diffeomorphisms on the torus, Trans. Amer. Math. Soc. 256(1979), 395-403. MR 546925 (80j:58041)
  • [B-F] P. Blanchard and J. Franks, The dynamical complexity of orientation reversing homeomorphisms of surfaces (preprint). MR 595592 (82f:58073)
  • [F] J. Franks, Some smooth maps with infinitely many hyperbolic periodic points, Trans. Amer. Math. Soc. 226(1977), 175-179. MR 0436221 (55:9169)
  • [H] M. Handel, The entropy of orientation reversing homeomorphisms of surfaces (preprint). MR 649760 (84f:58097)
  • [M] W. Massey, Algebraic topology: An introduction, Harcourt, Brace and World, New York, 1967. MR 0211390 (35:2271)
  • [N] C. Narasimhan, The periodic behavior of Morse-Smale diffeomorphisms on compact surfaces, Trans. Amer. Math. Soc. 248(1979), 145-169. MR 521698 (80g:58037)
  • [N] Z. Nitecki, Differentiable dynamics, M.I.T. Press, Cambridge, Mass., 1971. MR 0649788 (58:31210)
  • [P] J. Palis, On Morse-Smale dynamical systems, Topology 8(1969), 385-405. MR 0246316 (39:7620)
  • [P-S] J. Palis and S. Smale, Structural stability theorems, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., Providence, R.I., 1970, pp. 223-231. MR 0267603 (42:2505)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58F09

Retrieve articles in all journals with MSC: 58F09


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1981-0597864-0
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society