Some examples of nonsingular Morse-Smale vector fields on S 3

F. Wesley Wilson Jr

Annales de l'institut Fourier (1977)

  • Volume: 27, Issue: 2, page 145-159
  • ISSN: 0373-0956

Abstract

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One wonders or not whether it is possible to determine the homotopy class of a vector field by examining some algebraic invariants associated with its qualitative behavior. In this paper, we investigate the algebraic invariants which are usually associated with the periodic solutions of non-singular Morse-Smale vector fields on the 3-sphere. We exhibit some examples for which there appears to be no correlation between the algebraic invariants of the periodic solutions and the homotopy classes of the vector fields.

How to cite

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Wilson Jr, F. Wesley. "Some examples of nonsingular Morse-Smale vector fields on $S^3$." Annales de l'institut Fourier 27.2 (1977): 145-159. <http://eudml.org/doc/74314>.

@article{WilsonJr1977,
abstract = {One wonders or not whether it is possible to determine the homotopy class of a vector field by examining some algebraic invariants associated with its qualitative behavior. In this paper, we investigate the algebraic invariants which are usually associated with the periodic solutions of non-singular Morse-Smale vector fields on the 3-sphere. We exhibit some examples for which there appears to be no correlation between the algebraic invariants of the periodic solutions and the homotopy classes of the vector fields.},
author = {Wilson Jr, F. Wesley},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {145-159},
publisher = {Association des Annales de l'Institut Fourier},
title = {Some examples of nonsingular Morse-Smale vector fields on $S^3$},
url = {http://eudml.org/doc/74314},
volume = {27},
year = {1977},
}

TY - JOUR
AU - Wilson Jr, F. Wesley
TI - Some examples of nonsingular Morse-Smale vector fields on $S^3$
JO - Annales de l'institut Fourier
PY - 1977
PB - Association des Annales de l'Institut Fourier
VL - 27
IS - 2
SP - 145
EP - 159
AB - One wonders or not whether it is possible to determine the homotopy class of a vector field by examining some algebraic invariants associated with its qualitative behavior. In this paper, we investigate the algebraic invariants which are usually associated with the periodic solutions of non-singular Morse-Smale vector fields on the 3-sphere. We exhibit some examples for which there appears to be no correlation between the algebraic invariants of the periodic solutions and the homotopy classes of the vector fields.
LA - eng
UR - http://eudml.org/doc/74314
ER -

References

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  9. [9] C. PUGH, R. WALKER and F. W. WILSON, On Morse-Smale approximations: a counter example, Jour. Diff. Equations, to appear. Zbl0346.58006
  10. [10] B. L. REINHART, Line elements on the torus, Am. J. Math., 81 (1959), 617-631. Zbl0098.29006MR22 #1915
  11. [11] S. SMALE, Differential dynamical systems, Bull. A.M.S., 73 (1967), 747-817. Zbl0202.55202
  12. [12] F. W. WILSON, Some examples of vector fields on the 3-sphere, Ann. Four. Inst., Grenoble, 20 (1970), 1-20. Zbl0195.25403MR44 #3340
  13. [13] F. W. WILSON, On the minimal sets of nonsingular vector fields, Ann. Math., 84 (1966), 529-536. Zbl0156.43803MR34 #2028

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