Development of a metric for structural data is a long-term problem in pattern recognition and machine learning. In this talk, we develop a general metric for comparing nonlinear dynamical systems that is defined with Perron-Frobenius operator in reproducing kernel Hilbert spaces. Our metric includes the existing fundamental metrics for dynamical systems, which are basically defined with principal angles between some appropriately-chosen subspaces, as its special cases. We also describe the estimation of our metric from finite data. We empirically illustrate our metric with an example of rotation dynamics in a unit disk in a complex plane, and evaluate the performance with real-world time-series data. This work is based on a joint work with I.Ishikawa(RIKEN/Keio), K.Fujii(Nagoya), Y.Hashimoto(NTT) and　Y.Kawahara(Kyusyu/RIKEn) and is published in Proc. of NeurIPS 2018.