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unstable set

Proceedings of the Edinburgh Mathematical Society (1)

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Unstable sets, heteroclinic orbits and generic quasi-convergence for essentially strongly order-preserving semiflows
Part of
- Partial differential equations
- Qualitative theory
Taishan Yi, Qingguo Li
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 52 / Issue 3 / October 2009

Published online by Cambridge University Press:

23 September 2009, pp. 797-807
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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.