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Dynamical systems, filtrations and entropy
Author:
M. Shub
Journal:
Bull. Amer. Math. Soc. 80 (1974), 27-41
MSC (1970):
Primary 58F10, 58F20; Secondary 57D65
MathSciNet review:
0334284
Full-text PDF
References |
Similar Articles |
Additional Information
- 1.
R.
Abraham and S.
Smale, Nongenericity of Ω-stability, Global Analysis
(Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968), Amer. Math.
Soc., Providence, R.I., 1970, pp. 5–8. MR 0271986
(42 #6867)
- 2.
Rufus
Bowen, Topological entropy and axiom 𝐴, Global
Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968),
Amer. Math. Soc., Providence, R.I., 1970, pp. 23–41. MR 0262459
(41 #7066)
- 3.
Rufus
Bowen, Markov partitions for Axiom 𝐴 diffeomorphisms,
Amer. J. Math. 92 (1970), 725–747. MR 0277003
(43 #2740)
- 4.
Rufus
Bowen, Entropy for group endomorphisms and
homogeneous spaces, Trans. Amer. Math. Soc.
153 (1971),
401–414. MR 0274707
(43 #469), http://dx.doi.org/10.1090/S0002-9947-1971-0274707-X
- 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. MR 0271990
(42 #6871)
- 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, 1977. MR 0501173
(58 #18595)
- 8.
Anthony
Manning, Axiom 𝐴 diffeomorphisms have rational zeta
functions, Bull. London Math. Soc. 3 (1971),
215–220. MR 0288786
(44 #5982)
- 9.
Sheldon
E. Newhouse, Diffeomorphisms with infinitely many sinks,
Topology 13 (1974), 9–18. MR 0339291
(49 #4051)
- 10.
Zbigniew
Nitecki, On semi-stability for diffeomorphisms, Invent. Math.
14 (1971), 83–122. MR 0293671
(45 #2748)
- 11.
Z.
Nitecki and M.
Shub, Filtrations, decompositions, and explosions, Amer. J.
Math. 97 (1975), no. 4, 1029–1047. MR 0394762
(52 #15561)
- 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. MR 0267603
(42 #2505)
- 13.
Charles
C. Pugh, An improved closing lemma and a general density
theorem, Amer. J. Math. 89 (1967), 1010–1021.
MR
0226670 (37 #2257)
- 14.
Charles
Pugh and Michael
Shub, The Ω-stability theorem for flows, Invent. Math.
11 (1970), 150–158. MR 0287579
(44 #4782)
- 15.
J.
W. Robbin, A structural stability theorem, Ann. of Math. (2)
94 (1971), 447–493. MR 0287580
(44 #4783)
- 16.
Michael
Shub, Endomorphisms of compact differentiable manifolds, Amer.
J. Math. 91 (1969), 175–199. MR 0240824
(39 #2169)
- 17.
Michael
Shub, Structurally stable diffeomorphisms
are dense, Bull. Amer. Math. Soc. 78 (1972), 817–818. MR 0307278
(46 #6398), http://dx.doi.org/10.1090/S0002-9904-1972-13047-7
- 18.
M.
Shub and S.
Smale, Beyond hyperbolicity, Ann. of Math. (2)
96 (1972), 587–591. MR 0312001
(47 #563)
- 19.
M.
Shub and D.
Sullivan, Homology theory and dynamical systems, Topology
14 (1975), 109–132. MR 0400306
(53 #4141)
- 20.
S.
Smale, On the structure of manifolds, Amer. J. Math.
84 (1962), 387–399. MR 0153022
(27 #2991)
- 21.
S.
Smale, Differentiable dynamical
systems, Bull. Amer. Math. Soc. 73 (1967), 747–817. MR 0228014
(37 #3598), http://dx.doi.org/10.1090/S0002-9904-1967-11798-1
- 22.
S.
Smale, The Ω-stability theorem, Global Analysis (Proc.
Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968), Amer. Math. Soc.,
Providence, r.I., 1970, pp. 289–297. MR 0271971
(42 #6852)
- 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. MR 0339222
(49 #3984)
- 24.
C.
T. C. Wall, Classification of (𝑛-1)-connected
2𝑛-manifolds, Ann. of Math. (2) 75 (1962),
163–189. MR 0145540
(26 #3071)
- 1.
- R. Abraham and S. Smale, Nongenericity of Ω-stability, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc, Providence, R.I., 1970, pp. 5-8. MR 42 #6867. MR 271986
- 2.
- R. Bowen, Topological entropy and Axiom A, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., Providence, R.I., 1970, pp. 23-41. MR 41 #7066. MR 262459
- 3.
- R. Bowen, Markov partitions for Axiom A diffeomorphisms, Amer. J. Math. 92 (1970), 725-747. MR 43 #2740. MR 277003
- 4.
- R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401-414. MR 43 #469. MR 274707
- 5.
- J. Franks, Anosov diffeomorphisms, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., Providence, R.I., 1970, pp. 61-93. MR 42 #6871. MR 271990
- 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 (to appear). MR 501173
- 8.
- A. Manning, Axiom A diffeomorphisms have rational zeta functions, Bull. London Math. Soc. 3 (1971), 215-220. MR 44 #5982. MR 288786
- 9.
- S. Newhouse, Diffeomorphisms with infinitely many sinks (to appear). MR 339291
- 10.
- Z. Nitecki, On semi-stability for diffeomorphisms, Invent. Math. 14 (1971), 83-122. MR 45 #2748. MR 293671
- 11.
- Z. Nitecki and M. Shub, Filtrations, decompositions, and explosions. Amer. J. Math. (to appear). MR 394762
- 12.
- J. Palis and S. Smale, Structural stability theorems, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., Providence, R.I., 1970, pp. 223-231. MR 42 #2505. MR 267603
- 13.
- C. C. Pugh, An improved closing lemma and a general density theorem, Amer. J. Math. 89 (1967), 1010-1021. MR 37 #2257. MR 226670
- 14.
- C. C. Pugh and M. Shub, The Ω-stability theorem for flows, Invent. Math. 11 (1970), 150-158. MR 44 #4782. MR 287579
- 15.
- J. Robbins, A structural stability theorem, Ann. of Math. (2) 94 (1971), 447-493. MR 44 #4783. MR 287580
- 16.
- M. Shub, Endomorphisms of compact differentiable manifolds, Amer. J. Math. 91 (1969), 175-199. MR 39 #2169. MR 240824
- 17.
- M. Shub, Structurally stable diffeomorphisms are dense, Bull. Amer. Math. Soc. 78 (1972), 817. MR 307278
- 18.
- M. Shub and S. Smale, Beyond hyperbolicity, Ann. of Math. (2) 96 (1972), 587. MR 312001
- 19.
- M. Shub and D. Sullivan, Homology theory and dynamical systems (to appear). MR 400306
- 20.
- S. Smale, On the structure of manifolds, Amer. J. Math. 84 (1962), 387-399. MR 27 #2991. MR 153022
- 21.
- S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817. MR 37 #3598. MR 228014
- 22.
- S. Smale, The Ω-stability theorem, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., Providence, R.I., 1970, pp. 289-297. MR 42 #6852. MR 271971
- 23.
- S. Smale, Stability and isotopy in discrete dynamical systems, Proc. Sympos. on Dynamical Systems, Salvador, Brazil, 1971. (to appear). MR 339222
- 24.
- C. T. C. Wall, Classification of (n-1)-connected 2n-manifolds, Ann. of Math. (2) 75 (1962), 163-189. MR 26 #3071. MR 145540
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9904-1974-13344-6
PII:
S 0002-9904(1974)13344-6
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