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

How to cite

top

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

top
  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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.