An auto-homeomorphism of a Cantor set with derivative zero everywhere

作者：Ciesielski Krzysztof Chris; Jasinski Jakub^*

来源：Journal of Mathematical Analysis and Applications, 2016, 434(2): 1267-1280.

DOI：10.1016/j.jmaa.2015.09.076

• Differentiable minimal dynamical systems
• Fixed point theorem

We construct a closed bounded subset x of R with no isolated points which admits a differentiable bijection f: x -> x such that f'(x) = 0 for all x is an element of x. We also show that any such function admits a restriction f (sic) P to an uncountable closed P subset of x forming a minimal dynamical system. The existence of such a map f seems to contradict several well know results. The map f marks a limit beyond which Banach Fixed-Point Theorem cannot be generalized.

• 出版日期2016-2-15