Stable manifolds for differential equations and diffeomorphisms

S. Smale

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1963)

  • Volume: 17, Issue: 1-2, page 97-116
  • ISSN: 0391-173X

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Smale, S.. "Stable manifolds for differential equations and diffeomorphisms." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 17.1-2 (1963): 97-116. <http://eudml.org/doc/83301>.

@article{Smale1963,
author = {Smale, S.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {ordinary differential equations},
language = {eng},
number = {1-2},
pages = {97-116},
publisher = {Scuola normale superiore},
title = {Stable manifolds for differential equations and diffeomorphisms},
url = {http://eudml.org/doc/83301},
volume = {17},
year = {1963},
}

TY - JOUR
AU - Smale, S.
TI - Stable manifolds for differential equations and diffeomorphisms
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1963
PB - Scuola normale superiore
VL - 17
IS - 1-2
SP - 97
EP - 116
LA - eng
KW - ordinary differential equations
UR - http://eudml.org/doc/83301
ER -

References

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  1. 1 G.D. Birkhoff, Collected Mathematical PapersNew York1950. Zbl0041.34201
  2. 2 Coddington and Levinson, Theory of Ordinary differential equations, McGraw-Hill, New York1955. Zbl0064.33002MR69338
  3. 3 L.E. Elsgoltz, An estimate for the number of singular points of a dynamical system defined on a manifold, Amer. Math. Soc. Translation No. 68, 1952. MR47263
  4. 4 P. Hartman, On local homeomorphisms of Euclidean space, Proceedings of the Symposium on Ordinary Differential Equations, Mexico City, 1959. Zbl0127.30202MR141856
  5. 5 S. Lefschetz, Differential Equations, Geometric Theory, New York1957. Zbl0080.06401MR94488
  6. 6 D.C. Lewis, Invariant manifolds near an invariant point of unstable type, Amer. Journal Math. Vol. 60 (1938) pp. 577-587. Zbl0019.06501MR1507339JFM64.0708.02
  7. 7 R.S. Palais, Local Triviality of the restriction map for embeddings, Comm. Math Helv. Vol. 34 (1960) pp. 305-312. Zbl0207.22501MR123338
  8. 8 M. Peixoto, On structural stabililyAnn. of Math. Vol. 69 (1959) pp. 199-222. Zbl0084.08403MR101951
  9. 9 M. Peixoto, Structural stability on 2-dimensional manifolds, Topology Vol. 2 (1962) pp. 101-121. Zbl0107.07103MR142859
  10. 10 I. Petrovsky, On the behavior of the integral curves of a system of differential equations in the neighbourhood of singular point. Rec. Math. (Mat. Sbornik) N. S. Vol. 41-(1934) pp. 107-155. 
  11. 11 G. Reeb, Sur certaines propriétés topologiques des projectoires de8 systemes dynamiques, Acad. Roy. Belg. Cl. Sci. Mem. Coll.8° 27 N° 9, (1952). Zbl0048.32903MR58202
  12. 12 S. Smale, Morse inequalities for a dynamical system, Bull Amer. Math. Soc. Vol. 48 (1940) pp. 883-890. Zbl0100.29701MR117745
  13. 13 S. Smale, On Gradient Dynamical Systems, Ann. of Math. Vol. 74 (1961) pp. 199-206. Zbl0136.43702MR133139
  14. 14 S. Sternberg, Local contractions and a theorem of Poincaré, Amer. Journ. Math, Vol. 79 (1957) pp. 809-824. Zbl0080.29902MR96853
  15. 15 R. Thom, Sur une partition en cellules associee à une function sur une variété, C. R. Acad. Sci. Paris Vol. 228 (1949) pp. 973-975. Zbl0034.20802MR29160
  16. 16 R. Thom, Quelques propriétés globoles des variétés differentiables, Comm. Math. Helv., 28 (1954), pp. 17-86. Zbl0057.15502MR61823
  17. 17 R. Abraham, Transversality of manifolds of mappings to appear. Zbl0171.44501
  18. 18 L. Marcus, Structurally stable differential systems, Ann. of Math. Vol. 73 (1961) pp. 1-19. Zbl0131.31504MR132888

Citations in EuDML Documents

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  1. Claude Godbillon, Travaux de D. Anosov et S. Smale sur les difféomorphismes
  2. Jorge Sotomayor, Generic one-parameter families of vector fields on two-dimensional manifolds
  3. Maxime Percie du Sert, Une classe de systèmes dynamiques monotones génériquement Morse-Smale
  4. Sheldon E. Newhouse, Jacob Palis, Floris Takens, Bifurcations and stability of families of diffeomorphisms
  5. Sylvain Crovisier, Periodic orbits and chain-transitive sets of C1-diffeomorphisms
  6. Norman E. Hurt, Topology of quantizable dynamical systems and the algebra of observables

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