Orientation-reversing Morse-Smale diffeomorphisms on the torus

Batterson, Steve

doi:10.1090/S0002-9947-1981-0597864-0

Orientation-reversing Morse-Smale diffeomorphisms on the torus
HTML articles powered by AMS MathViewer

by Steve Batterson

Trans. Amer. Math. Soc. 264 (1981), 29-37

DOI: https://doi.org/10.1090/S0002-9947-1981-0597864-0

PDF | Request permission

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

Steve Batterson, The dynamics of Morse-Smale diffeomorphisms on the torus, Trans. Amer. Math. Soc. 256 (1979), 395–403. MR 546925, DOI 10.1090/S0002-9947-1979-0546925-1
Paul Blanchard and John Franks, The dynamical complexity of orientation-reversing homeomorphisms of surfaces, Invent. Math. 62 (1980/81), no. 2, 333–339. MR 595592, DOI 10.1007/BF01389164
John M. Franks, Some smooth maps with infinitely many hyperbolic periodic points, Trans. Amer. Math. Soc. 226 (1977), 175–179. MR 436221, DOI 10.1090/S0002-9947-1977-0436221-3
Michael Handel, The entropy of orientation reversing homeomorphisms of surfaces, Topology 21 (1982), no. 3, 291–296. MR 649760, DOI 10.1016/0040-9383(82)90011-8
William S. Massey, Algebraic topology: An introduction, Harcourt, Brace & World, Inc., New York, 1967. MR 0211390
Carolyn C. Narasimhan, The periodic behavior of Morse-Smale diffeomorphisms on compact surfaces, Trans. Amer. Math. Soc. 248 (1979), no. 1, 145–169. MR 521698, DOI 10.1090/S0002-9947-1979-0521698-7
Zbigniew Nitecki, Differentiable dynamics. An introduction to the orbit structure of diffeomorphisms, The M.I.T. Press, Cambridge, Mass.-London, 1971. MR 0649788
J. Palis, On Morse-Smale dynamical systems, Topology 8 (1968), 385–404. MR 246316, DOI 10.1016/0040-9383(69)90024-X
J. Palis and S. Smale, Structural stability theorems, Global Analysis (Proc. Sympos. Pure Math., Vols. XIV, XV, XVI, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 223–231. MR 0267603