A 3-dimensional Abraham-Smale example

Simon, Carl P.

doi:10.1090/S0002-9939-1972-0295391-1

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A $3$-dimensional Abraham-Smale example
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by Carl P. Simon PDF

Proc. Amer. Math. Soc. 34 (1972), 629-630 Request permission

Abstract:

The author constructs an open set of non $\Omega$-stable diffeomorphisms on ${T^3}$.

References

R. Abraham and S. Smale, Nongenericity of $\Omega$-stability, Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 5–8. MR 0271986
S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747–817. MR 228014, DOI 10.1090/S0002-9904-1967-11798-1
R. F. Williams, The $“\textrm {DA}''$ maps of Smale and structural stability, Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 329–334. MR 0264705