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.
  • #1
codebpr
6
0
TL;DR Summary
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?
 

Similar threads

A "Monstrous Higgs and Leech Spacetime"
    • Beyond the Standard Models
Replies
0
Views
1K
I Trying To Conceptualize Two Dimensions Of Time
    • Beyond the Standard Models
Replies
2
Views
2K
I Two recent tests of loop quantum gravity theory
    • Beyond the Standard Models
Replies
9
Views
486
A The Exceptional Jordan Algebra in physics
    • Beyond the Standard Models
Replies
3
Views
1K
I Rovelli on Quantum Gravity
    • Beyond the Standard Models
4
Replies
105
Views
10K
A Twistors and celestial holography
    • Beyond the Standard Models
Replies
14
Views
3K
I Is this thesis a plausible explanation for muon weirdness?
    • Beyond the Standard Models
Replies
2
Views
2K
I Testing string/m-theory extra dimensions prediction
    • Beyond the Standard Models
Replies
10
Views
2K
I M-theory and loop quantization of higher dimensional SUGRA
    • Beyond the Standard Models
Replies
24
Views
4K
What Are the Current Trends in String Theory Research?
    • Beyond the Standard Models
2
Replies
41
Views
12K

Hot Threads

Recent Insights

Back
Top