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Unstable sets, heteroclinic orbits and generic quasi-convergence for essentially strongly order-preserving semiflows
Published online by Cambridge University Press: 23 September 2009
Abstract
We present conditions guaranteeing the existence of non-trivial unstable sets for compact invariant sets in semiflows with certain compactness conditions, and then establish the existence of such unstable sets for an unstable equilibrium or a minimal compact invariant set, not containing equilibria, in an essentially strongly order-preserving semiflow. By appealing to the limit-set dichotomy for essentially strongly order-preserving semiflows, we prove the existence of an orbit connection from an equilibrium to a minimal compact invariant set, not consisting of equilibria. As an application, we establish a new generic convergence principle for essentially strongly order-preserving semiflows with certain compactness conditions.
MSC classification
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- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 3 , October 2009 , pp. 797 - 807
- Copyright
- Copyright © Edinburgh Mathematical Society 2009
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