### Abstract

We consider planar asymptotically autonomous ordinary differential equations and their limit equations. We show that thew-limit sets of an asymptotically autonomous equation get very close to having the same properties (of Poincare/Bendixson type) as the Γ-limit sets of the corresponding limit equation provided that the non-autonomous perturbation decreases to 0 fast enough as time tends to infinity.

Original language | English (US) |
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Pages (from-to) | 1625-1640 |

Number of pages | 16 |

Journal | Differential and Integral Equations |

Volume | 7 |

Issue number | 5-6 |

State | Published - Nov 1994 |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics