## Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems.(English)Zbl 0755.58039

Let $$X$$ be a strongly ordered Banach space and $$F : X \to X$$ a compact $$C^{ 1,\alpha}$$-map such that for any $$x \in X$$ the derivative $$F'(x)$$ is a strongly positive operator. Assume that any compact invariant set admits continuous separation, a quite technical condition introduced in the paper. Let $$G$$ be a bounded positively invariant set. Then, the set of points from $$G$$ having their $$\omega$$-limit sets equal to a periodic orbit contains an open and dense set in $$G$$.
Reviewer: J.Ombach (Kraków)

### MSC:

 37C70 Attractors and repellers of smooth dynamical systems and their topological structure

### Keywords:

monotone dynamical systems; generic properties
Full Text:

### References:

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