### Abstract

We introduce the notion of a strongly bounded vector field, which is closely related to the usual notion of a bounded vector field, and we prove that any C1 strongly bounded vector field in rn with finitely many critical points satisfies that the sum of the indices of the vector field at these critical points is equal to (–1)n. In the planar case we improve this result since we prove it for C1 bounded vector fields. Moreover, when n ≥ 3, we present examples of C∞ bounded vector fields in rn, being obviously not strongly bounded, not satisfying that the sum of the indices at the critical points is (-1)n. © 1999 Rocky Mountain Mathematics Consortium.

Original language | English |
---|---|

Pages (from-to) | 473-489 |

Journal | Rocky Mountain Journal of Mathematics |

Volume | 29 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jan 1999 |

### Keywords

- Bounded vector field
- Index

## Fingerprint Dive into the research topics of 'On bounded vector fields'. Together they form a unique fingerprint.

## Cite this

Cima, A., Mañosas, F., & Villadelprat, J. (1999). On bounded vector fields.

*Rocky Mountain Journal of Mathematics*,*29*(2), 473-489. https://doi.org/10.1216/rmjm/1181071647