×

zbMATH — the first resource for mathematics

Dynamical systems, filtrations and entropy. (English) Zbl 0305.58014

MSC:
37D99 Dynamical systems with hyperbolic behavior
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] 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
[2] Rufus Bowen, Topological entropy and axiom \?, Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968), Amer. Math. Soc., Providence, R.I., 1970, pp. 23 – 41.
[3] Rufus Bowen, Markov partitions for Axiom \? diffeomorphisms, Amer. J. Math. 92 (1970), 725 – 747. · Zbl 0208.25901 · doi:10.2307/2373370 · doi.org
[4] Rufus Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401 – 414. · Zbl 0212.29201
[5] John Franks, Anosov diffeomorphisms, Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968), Amer. Math. Soc., Providence, R.I., 1970, pp. 61 – 93. · Zbl 0207.54304
[6] F. Gantmacher, The theory of matrices, GITTL, Moscow, 1953; English transl., Vol. 2, Chelsea, New York, 1959. MR 16, 438; 21 #6372c.
[7] M. W. Hirsch, C. C. Pugh, and M. Shub, Invariant manifolds, Lecture Notes in Mathematics, Vol. 583, Springer-Verlag, Berlin-New York, 1977. · Zbl 0355.58009
[8] Anthony Manning, Axiom \? diffeomorphisms have rational zeta functions, Bull. London Math. Soc. 3 (1971), 215 – 220. · Zbl 0219.58007 · doi:10.1112/blms/3.2.215 · doi.org
[9] Sheldon E. Newhouse, Diffeomorphisms with infinitely many sinks, Topology 13 (1974), 9 – 18. · Zbl 0275.58016 · doi:10.1016/0040-9383(74)90034-2 · doi.org
[10] Zbigniew Nitecki, On semi-stability for diffeomorphisms, Invent. Math. 14 (1971), 83 – 122. · Zbl 0218.58007 · doi:10.1007/BF01405359 · doi.org
[11] Z. Nitecki and M. Shub, Filtrations, decompositions, and explosions, Amer. J. Math. 97 (1975), no. 4, 1029 – 1047. · Zbl 0324.58015 · doi:10.2307/2373686 · doi.org
[12] 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
[13] Charles C. Pugh, An improved closing lemma and a general density theorem, Amer. J. Math. 89 (1967), 1010 – 1021. · Zbl 0167.21804 · doi:10.2307/2373414 · doi.org
[14] Charles Pugh and Michael Shub, The \Omega -stability theorem for flows, Invent. Math. 11 (1970), 150 – 158. · Zbl 0212.29102 · doi:10.1007/BF01404608 · doi.org
[15] J. W. Robbin, A structural stability theorem, Ann. of Math. (2) 94 (1971), 447 – 493. · Zbl 0224.58005 · doi:10.2307/1970766 · doi.org
[16] Michael Shub, Endomorphisms of compact differentiable manifolds, Amer. J. Math. 91 (1969), 175 – 199. · Zbl 0201.56305 · doi:10.2307/2373276 · doi.org
[17] Michael Shub, Structurally stable diffeomorphisms are dense, Bull. Amer. Math. Soc. 78 (1972), 817 – 818. · Zbl 0265.58003
[18] M. Shub and S. Smale, Beyond hyperbolicity, Ann. of Math. (2) 96 (1972), 587 – 591. · Zbl 0247.58008 · doi:10.2307/1970826 · doi.org
[19] M. Shub and D. Sullivan, Homology theory and dynamical systems, Topology 14 (1975), 109 – 132. · Zbl 0408.58023 · doi:10.1016/0040-9383(75)90022-1 · doi.org
[20] S. Smale, On the structure of manifolds, Amer. J. Math. 84 (1962), 387 – 399. · Zbl 0109.41103 · doi:10.2307/2372978 · doi.org
[21] S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747 – 817. · Zbl 0202.55202
[22] 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.
[23] Steve Smale, Stability and isotopy in discrete dynamical systems, Dynamical systems (Proc. Sympos., Univ. Bahia, Salvador, 1971) Academic Press, New York, 1973, pp. 527 – 530.
[24] C. T. C. Wall, Classification of (\?-1)-connected 2\?-manifolds, Ann. of Math. (2) 75 (1962), 163 – 189. · Zbl 0218.57022 · doi:10.2307/1970425 · doi.org
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.