| Contents |
| The talk deals with the classical concept of a continuous separation over a compact positively-invariant set $K$
of a monotone and $C^1$ skew-product semiflow, as well as with a recently introduced new concept which is useful in applications to delay equations. Sufficient conditions are given in terms of the linearized operators over $K$ and some practical criteria for non-autonomous recurrent differential equations are presented.
When a continuous separation over $K$ exists, the uniform persistence of the semiflow in the areas situated strongly above and strongly below $K$ can be determined by means of the principal spectrum. Besides, we show how to manage general cooperative systems when in principle there is no continuous separation. Finally, we show how to numerically compute the leading direction of the continuous separation. |
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