Lyapunov exponents

Trajectory divergence rates

Lyapunov exponents measure how sensitive a dynamical system is to small changes in initial conditions—how quickly nearby trajectories diverge or converge over time.

A positive exponent indicates chaos: tiny differences grow exponentially, making long-term prediction impossible.

A negative exponent means trajectories converge toward stability.

Systems have as many Lyapunov exponents as they have dimensions, and the largest one determines overall predictability.

The positive Lyapunov exponent confirmed the system was chaotic.

Related

dynamics · singularities · Poincaré map · tangent · differential equations · strange attractors · initial conditions · nonlinearity · divergences · manifolds · orbits · butterfly effect · predictability · sensitive dependence · critical points · deterministic chaos · Lorenz · spectrum

Categories
Opposites
dynamical behavior indicated

Lyapunov exponentsstability

Resistance to displacement

convergence · attractors · dissipation · contraction · damping

system characterization approach

Lyapunov exponentsconservation laws

Quantities unchanged through time

structural stability

Family

Lyapunov exponent, exponent, exponential, exponentially, exponents, exponentiation

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