The dynamics of Morse-Smale diffeomorphisms on the torus
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- by Steve Batterson PDF
- Trans. Amer. Math. Soc. 256 (1979), 395-403 Request permission
Abstract:
For orientation preserving 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, Structurally stable Grassmann transformations, Trans. Amer. Math. Soc. 231 (1977), no. 2, 385–404. MR 448443, DOI 10.1090/S0002-9947-1977-0448443-6
- 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
- John Franks and Carolyn Narasimhan, The periodic behavior of Morse-Smale diffeomorphisms, Invent. Math. 48 (1978), no. 3, 279–292. MR 508988, DOI 10.1007/BF01390247
- J. Myron Masley and Hugh L. Montgomery, Cyclotomic fields with unique factorization, J. Reine Angew. Math. 286(287) (1976), 248–256. MR 429824
- John Milnor, Lectures on the $h$-cobordism theorem, Princeton University Press, Princeton, N.J., 1965. Notes by L. Siebenmann and J. Sondow. MR 0190942, DOI 10.1515/9781400878055
- 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
- Morris Newman, Integral matrices, Pure and Applied Mathematics, Vol. 45, Academic Press, New York-London, 1972. MR 0340283
- J. Palis and S. Smale, Structural stability theorems, Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 223–231. MR 0267603 L. da Rocha, Caracterizacao das classes de isotopia Morse-Smale em superficies, Thesis, IMPA, 1978.
- M. Shub, Morse-Smale diffeomorphisms are unipotent on homology, Dynamical systems (Proc. Sympos., Univ. Bahia, Salvador, 1971) Academic Press, New York, 1973, pp. 489–491. MR 0331439
- M. Shub and D. Sullivan, Homology theory and dynamical systems, Topology 14 (1975), 109–132. MR 400306, DOI 10.1016/0040-9383(75)90022-1
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 256 (1979), 395-403
- MSC: Primary 58F09; Secondary 58F20, 58F22
- DOI: https://doi.org/10.1090/S0002-9947-1979-0546925-1
- MathSciNet review: 546925