Does the Maximum Lyapunov exponent depend on the eigenvalues?

In summary, the Maximum Lyapunov exponent is a measure of the rate of separation between two trajectories in a dynamical system and is used to quantify the level of chaos in a system. It is calculated by taking the logarithm of the ratio between the separation of two trajectories and their initial separation, divided by the time interval. The Maximum Lyapunov exponent is directly related to the eigenvalues of the Jacobian matrix, with higher values indicating a more chaotic and unstable system. Changes in the system's parameters can also affect the Maximum Lyapunov exponent. However, it cannot be used to predict the long-term behavior of a system, as it only measures short-term predictability.
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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:

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

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

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