### 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) |
---|---|

Pages (from-to) | 1625-1640 |

Number of pages | 16 |

Journal | Differential and Integral Equations |

Volume | 7 |

Issue number | 5-6 |

State | Published - 1994 |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

**Asymptotically autonomous differential equations in the plane II. Stricter Poincaré/Bendixson type results.** / Thieme, Horst.

Research output: Contribution to journal › Article

*Differential and Integral Equations*, vol. 7, no. 5-6, pp. 1625-1640.

}

TY - JOUR

T1 - Asymptotically autonomous differential equations in the plane II. Stricter Poincaré/Bendixson type results

AU - Thieme, Horst

PY - 1994

Y1 - 1994

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33746945861&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746945861&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33746945861

VL - 7

SP - 1625

EP - 1640

JO - Differential and Integral Equations

JF - Differential and Integral Equations

SN - 0893-4983

IS - 5-6

ER -