Absolutely structurally stable diffeomorphisms

Franks, John

doi:10.1090/S0002-9939-1973-0312528-7

Absolutely structurally stable diffeomorphisms
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by John Franks

Proc. Amer. Math. Soc. 37 (1973), 293-296

DOI: https://doi.org/10.1090/S0002-9939-1973-0312528-7

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Abstract:

This paper gives a proof that if a diffeomorphism is structurally stable in a strong sense then it satisfies Axiom A of S. Smale. This provides a weakened converse of a theorem of J. Robbin on structural stability.

References

James Eells Jr., A setting for global analysis, Bull. Amer. Math. Soc. 72 (1966), 751–807. MR 203742, DOI 10.1090/S0002-9904-1966-11558-6
John Franks, Differentiably $\Omega$-stable diffeomorphisms, Topology 11 (1972), 107–113. MR 296972, DOI 10.1016/0040-9383(72)90025-0

Manifolds of

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John Guckenheimer, Absolutely $\Omega$-stable diffeomorphisms, Topology 11 (1972), 195–197. MR 296973, DOI 10.1016/0040-9383(72)90006-7
J. W. Robbin, A structural stability theorem, Ann. of Math. (2) 94 (1971), 447–493. MR 287580, DOI 10.2307/1970766
Stephen Smale, Notes on differentiable dynamical systems, Global Analysis (Proc. Sympos. Pure Math., Vols. XIV, XV, XVI, Berkeley, Calif., 1968) Proc. Sympos. Pure Math., XIV-XVI, Amer. Math. Soc., Providence, RI, 1970, pp. 277–287. MR 266245