Newhouse, Sheldon E. Hyperbolic limit sets. (English) Zbl 0239.58009 Trans. Am. Math. Soc. 167, 125-150 (1972). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 36 Documents MSC: 37D99 Dynamical systems with hyperbolic behavior 37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics PDF BibTeX XML Cite \textit{S. E. Newhouse}, Trans. Am. Math. Soc. 167, 125--150 (1972; Zbl 0239.58009) Full Text: DOI References: [1] George D. Birkhoff, Dynamical systems, With an addendum by Jurgen Moser. American Mathematical Society Colloquium Publications, Vol. IX, American Mathematical Society, Providence, R.I., 1966. [2] Morris W. Hirsch and Charles C. Pugh, Stable manifolds and hyperbolic sets, Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968), Amer. Math. Soc., Providence, R.I., 1970, pp. 133 – 163. [3] M. Hirsch, J. Palis, C. Pugh, and M. Shub, Neighborhoods of hyperbolic sets, Invent. Math. 9 (1969/1970), 121 – 134. · Zbl 0191.21701 [4] J. Palis, On Morse-Smale dynamical systems, Topology 8 (1968), 385 – 404. · Zbl 0189.23902 [5] -, A note on \( \Omega \)-stability, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., Providence, R. I., 1970. MR 41 #7686. [6] 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. · Zbl 0214.50702 [7] Charles Pugh and Michael Shub, The \Omega -stability theorem for flows, Invent. Math. 11 (1970), 150 – 158. · Zbl 0212.29102 [8] J. W. Robbin, A structural stability theorem, Ann. of Math. (2) 94 (1971), 447 – 493. · Zbl 0224.58005 [9] Stephen Smale, Diffeomorphisms with many periodic points, Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), Princeton Univ. Press, Princeton, N.J., 1965, pp. 63 – 80. [10] S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747 – 817. · Zbl 0202.55202 [11] S. Smale, The \Omega -stability theorem, Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968), Amer. Math. Soc., Providence, r.I., 1970, pp. 289 – 297. [12] Zbigniew Nitecki, On semi-stability for diffeomorphisms, Invent. Math. 14 (1971), 83 – 122. · Zbl 0218.58007 [13] 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. · Zbl 0215.25102 [14] L. P. Šil\(^{\prime}\)nikov, On the question of the structure of the neighborhood of a homoclinic tube of an invariant torus, Dokl. Akad. Nauk SSSR 180 (1968), 286 – 289 (Russian). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.