First return path systems: Differentiability, continuity, and orderings
The study of first return path systems is continued. If \(f: [0, 1]\to \mathbb{R}\) is compositely differentiable to \(g\) and if for each \(x\in [0, 1]\quad g(x)\) is a bilateral derived number of \(f\) at \(x\) then \(f\) is universally first return differentiable to \(g\). A function \(f\) is first return continuous iff \(f\) is \(\text{DB}_ 1\). If \(f\in \text{DB}^*_ 1\) then \(f\) is universally first return continuous. Some examples are shown and it is proven that each first return path system can be generated from a trajectory of a continuous transitive mapping.
scientific article; zbMATH DE number 755494
scientific article