Projects per year

## Abstract

Let X:U â†’ R2 be a differentiable vector field. Set Spc(X) = {eigenvalues of DX(z): zâˆˆ U}. This X is called Hurwitz if Spc(X)âŠ‚{zâˆˆC:â„œ(z)<0}. Suppose that X is Hurwitz and UâŠ‚R2 is the complement of a compact set. Then by adding to X a constant v one obtains that the infinity is either an attractor or a repellor for X+v. That means: (i) there exists a unbounded sequence of closed curves, pairwise bounding an annulus the boundary of which is transversal to X+v, and (ii) there is a neighborhood of infinity with unbounded trajectories, free of singularities and periodic trajectories of X+v. This result is obtained after to proving the existence of X~:R2 â†’ R2, a topological embedding such that X~ equals X in the complement of some compact subset of U. Â© 2013 Elsevier Inc.

Original language | Spanish |
---|---|

Pages (from-to) | 1050-1066 |

Number of pages | 17 |

Journal | Journal of Differential Equations |

Volume | 255 |

State | Published - 1 Sep 2013 |

## Projects

- 1 Finished