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

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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 languageEnglish (US)
Pages (from-to)1625-1640
Number of pages16
JournalDifferential and Integral Equations
Volume7
Issue number5-6
StatePublished - 1994

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Ordinary differential equations
Differential equations
Limit Set
Differential equation
Poincaré
Ordinary differential equation
Infinity
Tend
Perturbation
Decrease

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

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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.",
author = "Horst Thieme",
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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.

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