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Periodic approximations and spectral analysis of the Koopman operator: theory and applications

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Figure

Figure 2.1: The hybrid pendulum: (top) upon passing the angle ±θ ∗ from below the pendulum experiences a change in angular velocity by ∆ω, (middle) the corresponding hybrid automaton representation, (bottom) the state-space of the system.
Figure 2.2: Basin of attraction for the limit cycle with p 1 = 0.7. p cr = 1.65 (top), p cr = 1.7 (bottom-left), p cr = 1.73 (bottom-right).
Figure 2.3: The dissipation function d computed for different viscous damping coeffi- coeffi-cients
Figure 2.4: Projections of observables onto the eigenspace of Koopman at λ = 0.
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