What is the difference between local and global Lyapunov exponents?
Conditions
- Comparison is with global Lyapunov exponents
- The limit is omitted
Reasoning, step by step
- Recall that global Lyapunov exponents are defined as long-term averages involving the limit .
- Understand that local Lyapunov exponents use the same basic idea of measuring stretching.
- Recognize that the infinite-time limit is removed from both the definition and the calculation for local exponents.
- Conclude that local exponents capture more spatial detail about how stretching varies from place to place.
Example
The speaker says "local Lyapunov exponents" are "exactly like global Lyapunov exponents except you take the limit as t goes to infinity out of the definition and out of the calculation". She adds they capture "a bit more spatial detail about how things" behave.
Common misconceptions
- Thinking local exponents are a completely different mathematical concept.
- Assuming global exponents capture fine-grained spatial variations.
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