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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  1. [1] D. ASIMOV, Round Handles and Nonsingular Morse-Smale Flows, to appear. 
  2. [2] A. DAVIS, Singular Foliations, Doctoral Dissertation, Univ. of Colorado, 1971. 
  3. [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
  4. [4] F. B. FULLER, Note on trajectories on a solid torus, Ann. Math., 56 (1952), 438-439. Zbl0047.08901MR14,556j
  5. [5] H. HOPF, Uber die abbildungen von Spharen auf Spharen neidrigerer dimension, Fund. Math., 25 (1935), 427-440. Zbl0012.31902JFM61.0622.04
  6. [6] J. PALIS and S. SMALE, Structural stability theorems, global analysis, A.M.S. Proc. Symp. Pure Math., 14 (1970), 223-231. Zbl0214.50702MR42 #2505
  7. [7] M. PEIXOTO, Structural stability on 2-dimensional manifolds, Topology, 1 (1962), 101-120. Zbl0107.07103MR26 #426
  8. [8] P. PERCELL and F. W. WILSON, Plugging Flows, to appear. Zbl0367.34037
  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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