Speaker
Description
The Koopman linearization enables the use of the linear operator theory in the study of nonlinear dynamical systems by switching from a topological dynamical system $(K, \varphi)$ to a Koopman system $(C(K), T_{\varphi})$ consisting of the space $C(K)$ of continuous complex-valued functions on $K$ and the composition operator $T_{\varphi} \colon f \mapsto f \circ \varphi$ on $C(K).$
Let $C_0(K)$ be the Banach space of all continuous complex-valued functions on a connected locally compact Hausdorff space $K$, vanishing at infinity. According to the classical Banach-Stone theorem, surjective linear isometries on $C_0(K)$ are weighted composition operators, that is, of the form $f \mapsto u(\,\cdot\,) \, f \circ \varphi$ for some continuous unimodular function $u \colon K \to \mathbb{C}$ and a homeomorphism $\varphi \colon K \to K$. In this talk, the spectrum of periodic linear isometries on $C_0(K)$ will be described.
