Bifurcation and stability of families of hyperbolic vector fields in dimension three

Sergio Plaza; Jaime Vera

Annales de l'I.H.P. Analyse non linéaire (1997)

  • Volume: 14, Issue: 1, page 119-142
  • ISSN: 0294-1449

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Plaza, Sergio, and Vera, Jaime. "Bifurcation and stability of families of hyperbolic vector fields in dimension three." Annales de l'I.H.P. Analyse non linéaire 14.1 (1997): 119-142. <http://eudml.org/doc/78403>.

@article{Plaza1997,
author = {Plaza, Sergio, Vera, Jaime},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {structural stability; hyperbolic vector field; spectral decomposition; bifurcation set},
language = {eng},
number = {1},
pages = {119-142},
publisher = {Gauthier-Villars},
title = {Bifurcation and stability of families of hyperbolic vector fields in dimension three},
url = {http://eudml.org/doc/78403},
volume = {14},
year = {1997},
}

TY - JOUR
AU - Plaza, Sergio
AU - Vera, Jaime
TI - Bifurcation and stability of families of hyperbolic vector fields in dimension three
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1997
PB - Gauthier-Villars
VL - 14
IS - 1
SP - 119
EP - 142
LA - eng
KW - structural stability; hyperbolic vector field; spectral decomposition; bifurcation set
UR - http://eudml.org/doc/78403
ER -

References

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  2. [La] R. Labarca, Stability of parametrized families of vector fields, Pitman Research Notes in Mathematics Series, Vol. 160, 1987, pp. 121-213. Zbl0632.58026MR907893
  3. [La-Pl] R. Labarca and S. Plaza, Global stability of vector fields, Erg. Theory and Dyn. Systems, Vol. 13, 1993, pp. 737-766. Zbl0798.58044MR1257032
  4. [Ma-P] I. Malta and J. Palis, Families of vector fields with finite modulus of stability, Lectures Notes in Math., Vol. 898, 1980, pp. 212-229. Zbl0482.58023MR654891
  5. [N] S. Newhouse, On simple arcs between structurally stable flows, Lectures Notes in Math., Vol. 468, 1975, pp. 209-233. Zbl0307.58011MR650638
  6. [N-P] S. Newhouse and J. Palis, Cycles and bifurcations theory, Asterisque, Vol. 31, 1976, pp. 44-140. Zbl0322.58009MR516408
  7. [N-P-T] S. Newhouse, J. Palis and F. Takens, Bifurcation and stability of families of diffeomorphisms, Publ. Math. I.H.E.S., Vol. 57, 1983, pp. 5-71. Zbl0518.58031MR699057
  8. [P-T] J. Palis and F. Takens, Stability of parametrized families of gradient vector fields, Ann. of Math., Vol. 118, 1983, pp. 383-421. Zbl0533.58018MR727698
  9. [Pl] S. Plaza, Global stability of saddle-node bifurcation of periodic orbit for vector fields, Annales de la Faculté de Sciences de Toulouse, Vol. III, n° 3, 1994, pp. 411-448. Zbl0831.58036MR1313357
  10. [Ro] J. Robin, Structural stability theorem, Annals of Math., Vol. 94, 1971, pp. 447-493. Zbl0224.58005MR287580
  11. [Rob] C. Robinson, Structurally stability for vector fields, Annals of Math., Vol. 99, 1974, pp. 154-175. Zbl0275.58012MR334283
  12. [Sm] S. Smale, Differentiable dynamical systems, Bull. A.M.S., Vol. 73, 1967, pp. 747- 817. Zbl0202.55202MR228014
  13. [Ta] F. Takens, Normal form for certain singularities of vector fields, Ann. Inst. Fourier, Vol. 23 (2), 1973, pp. 163-195. Zbl0266.34046MR365620
  14. [Ve] J. Vera, Stability of quasi-transversal bifurcation of vector fields on 3-dimensional manifolds, Preprint, 1994. 

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