Jaworski-type embedding theorems of one-sided dynamical systems
Tom 253 / 2021
Streszczenie
Embeddings of two-sided dynamical systems in the two-sided shift $(\mathbb R ^{\mathbb Z },\sigma )$ of the real line $\mathbb R $ have been studied by many authors. In this paper, we introduce the notion of trajectory-embedding for the one-sided shift $(\mathbb R ^{\mathbb N },\sigma )$ and we give trajectory-embedding theorems for some one-sided dynamical systems. In particular, we show that if $X$ is a finite-dimensional compact metric space and $T:X\to X$ is a doubly 0-dimensional map with at most 0-dimensional set ${\rm P} (T)$ of periodic points (i.e., $\dim {\rm P} (T)\leq 0$), then there is a trajectory-embedding of $(X,T)$ in $(\mathbb R ^{\mathbb N },\sigma )$. We study such embedding theorems of one-sided dynamical systems from a different perspective than Jaworski–Nerurkar–Gutman.
