What is the ordering convention for Lyapunov exponents?
Conditions
- n is the dimension of the dynamical system
- Ordering is by real value, not magnitude
Reasoning, step by step
- Identify all Lyapunov exponents of the system.
- Sort them by their actual real values on the number line.
- Assign the largest value (closest to positive infinity) to .
- Assign the next largest to , and so on.
- Assign the smallest value (closest to negative infinity) to .
Example
The speaker explicitly says the ordering is by closeness to positive infinity, not by magnitude, and identifies as closest to negative infinity. The blue handwritten vertical list shows , , vertical dots, .
Common misconceptions
- Confusing largest value with largest absolute value.
- Assuming is always positive.
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