A $\textbf {Z}\times \textbf {Z}$ structurally stable action
HTML articles powered by AMS MathViewer
- by P. R. Grossi Sad PDF
- Trans. Amer. Math. Soc. 260 (1980), 515-525 Request permission
Abstract:
We consider in the product of spheres ${S^m} \times {S^n}$ the $Z \times Z$-action generated by two simple Morse-Smale diffeomorphisms; if they have some kind of general position, the action is shown to be stable. An application is made to foliations.References
- Boyd Anderson, Diffeomorphisms with discrete centralizer, Topology 15 (1976), no. 2, 143–147. MR 402821, DOI 10.1016/0040-9383(76)90003-3
- César Camacho and Alcides Lins Neto, Orbit preserving diffeomorphisms and the stability of Lie group actions and singular foliations, Geometry and topology (Proc. III Latin Amer. School of Math., Inst. Mat. Pura Aplicada CNPq, Rio de Janeiro, 1976) Lecture Notes in Math., Vol. 597, Springer, Berlin, 1977, pp. 82–103. MR 0474407
- M. W. Hirsch, C. C. Pugh, and M. Shub, Invariant manifolds, Lecture Notes in Mathematics, Vol. 583, Springer-Verlag, Berlin-New York, 1977. MR 0501173, DOI 10.1007/BFb0092042
- Nancy Kopell, Commuting diffeomorphisms, Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 165–184. MR 0270396
- Richard S. Palais, Equivalence of nearby differentiable actions of a compact group, Bull. Amer. Math. Soc. 67 (1961), 362–364. MR 130321, DOI 10.1090/S0002-9904-1961-10617-4
- J. Palis, Rigidity of the centralizers of diffeomorphisms and structural stability of suspended foliations, Differential topology, foliations and Gelfand-Fuks cohomology (Proc. Sympos., Pontifícia Univ. Católica, Rio de Janeiro, 1976) Lecture Notes in Mathematics, Vol. 652, Springer, Berlin, 1978, pp. 114–121. MR 505654
- Charles Pugh and Michael Shub, Axiom $\textrm {A}$ actions, Invent. Math. 29 (1975), no. 1, 7–38. MR 377989, DOI 10.1007/BF01405171
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 260 (1980), 515-525
- MSC: Primary 58F10; Secondary 34C35, 58F30
- DOI: https://doi.org/10.1090/S0002-9947-1980-0574796-4
- MathSciNet review: 574796