  The analysis of nonlinear dynamics is an important issue in numerous fields
of science. In this study, we propose a new method to analyze the time series
data using persistent homology (PH). The key idea is the application of PH to
the distance matrix. Using this method, we can obtain the topological features
embedded in the trajectories. We apply this method to the logistic map,
R\"ossler system, and electrocardiogram data. The results reveal that our
method can effectively identify nonlocal characteristics of the attractor and
can classify data based on the amount of noise.
