关于双曲周期点与双曲周期轨的一种等价性及其证明

An Equivalence Property Between Hyperbolic Periodic Point and Hyperbolic Periodic Orbit and Its Proof

阐述双曲周期点与双曲周期轨的异同,指出双曲周期点与双曲周期轨之间的一种相互蕴含关系,并利用微分流形上微分同胚的保维数性质、复合微分同胚求导法则给予严格证明。

We elaborate the similarities and differences between hyperbolic periodic point and hyperbolic periodic orbit. Using the persisting property of dimension of differential homeomorphism and the derivative principle of composite homeomorphism, a rigorous proof is presented to imply the mutual equivalence between them.