A fixed point theorem for bounded dynamical systems

الأصل · EN

We show that a continuous map or a continuous flow on ⁿ with a certain recurrence relation must have a fixed point. Specifically, if there is a compact set W with the property that the forward orbit of every point in ⁿ intersects W then there is a fixed point in W. Consequently, if the omega limit set of every point is nonempty and uniformly bounded then there is a fixed point.