# Some examples of nonsingular Morse-Smale vector fields on ${S}^{3}$

Annales de l'institut Fourier (1977)

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

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topWilson 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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- [3] A. DAVIS and F. W. WILSON, Tangent vector fields to foliations I: Reeb foliations, Journal Diff. Equations, 11 (1972), 491-498. Zbl0242.57012MR46 #8238
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- [8] P. PERCELL and F. W. WILSON, Plugging Flows, to appear. Zbl0367.34037
- [9] C. PUGH, R. WALKER and F. W. WILSON, On Morse-Smale approximations: a counter example, Jour. Diff. Equations, to appear. Zbl0346.58006
- [10] B. L. REINHART, Line elements on the torus, Am. J. Math., 81 (1959), 617-631. Zbl0098.29006MR22 #1915
- [11] S. SMALE, Differential dynamical systems, Bull. A.M.S., 73 (1967), 747-817. Zbl0202.55202
- [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] F. W. WILSON, On the minimal sets of nonsingular vector fields, Ann. Math., 84 (1966), 529-536. Zbl0156.43803MR34 #2028

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