Unstable Manifolds of Continuous Self-Mappings

Abstract EN

Unstable manifolds of continuous self-mappings on completely densely ordered linear ordered topological spaces (CDOLOTS) are discussed.

Let f be a continuous self-map.

First, the interval with endpoints of two adjacent fixed points is contained in the unilateral unstable manifold of one of the endpoints.

Then, by using the above conclusion, we prove that periodic points of f not belong to the unstable manifold of their iteration points of fn (for some n∈ℕ), unless the iteration points are themselves.