Figure 7
The horizontal axis is labeled “Real Part” and ranges from negative 1.0 to 1.0 with an interval of 0.5. The vertical axis is labeled “Imaginary Part” and ranges from negative 1.0 to 1.0 with an interval of 0.5. A dashed circular boundary is centered at the origin with radius 1, forming a unit circle. Solid horizontal and vertical lines intersect at the origin, dividing the plane into four quadrants. Multiple red cross markers labeled “Eigenvalues (lambda)” are scattered within the circle. Several points are clustered near the right side close to the horizontal axis around a real value slightly greater than 0.6 and an imaginary value near 0. Additional points appear distributed across all quadrants, including positions near negative real values around negative 0.6 with both positive and negative imaginary parts, as well as points near the vertical axis slightly above and below the origin from between negative 0.5 and 0.5. The distribution forms a loose, uneven pattern with a noticeable concentration toward the right side. All points lie within the dashed unit circle labeled “Unit Circle (Boundary)”. Note: All numerical data values are approximated.Spectral analysis of the learned Koopman transition matrix A. The red markers denote the eigenvalues (λi) in the complex plane