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- Does the value of the Maximum Lyapunov exponent depend on the eigenvalues of the system?

I am currently reading this paper where on page 8, the authors say that:

Does it mean that there is a real correlation between eigenvalues and Lyapunov exponents?

This correlates with Figure 8 on page 12.Negative eigenvalues correspond to unstable systems.

Does it mean that there is a real correlation between eigenvalues and Lyapunov exponents?