Characteristic Lyapunov exponents and smooth ergodic theory¶
Pesin, Y. B. (1977). Characteristic Lyapunov exponents and smooth ergodic theory. Russian Mathematical Surveys, 32(4), 55-114.
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Primes¶
- Chaos
- … nearby states diverge exponentially fast on average; a small perturbation `δ_0` to the state grows roughly as `δ_t ≈ δ_0 · exp(λ t)` within a timescale set by the largest Lyapunov exponent `λ > 0`, with Pesin (1977) establishing the deep link between positive Lyapunov exponents and Kolmogorov-Sinai entropy
This sourceEstablishes Pesin's entropy formula relating Kolmogorov-Sinai entropy to the sum of positive Lyapunov exponents for smooth systems with SRB measures; the deep link between sensitive dependence and information-theoretic entropy.
- … nearby states diverge exponentially fast on average; a small perturbation `δ_0` to the state grows roughly as `δ_t ≈ δ_0 · exp(λ t)` within a timescale set by the largest Lyapunov exponent `λ > 0`, with Pesin (1977) establishing the deep link between positive Lyapunov exponents and Kolmogorov-Sinai entropy
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