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Local Lyapunov exponents are defined like global Lyapunov exponents but without taking the long-time limit $t\to\infty$, so they retain more spatial/local information about stretching.

Conditions: Comparison is with global Lyapunov exponents; The limit $t\to\infty$ is omitted

Local Lyapunov exponents are defined like global Lyapunov exponents but without taking the long-time limit $t\to\infty$, so they retain more spatial/local information about stretching.

Conditions: Comparison is with global Lyapunov exponents; The limit $t\to\infty$ is omitted

Exponential growth of separation on a bounded attractor is compatible with boundedness because the relevant measurement is local transverse stretching with renormalization along the attractor, not unlimited separation in the ambient space.

Conditions: The trajectory lies on an attractor; Separation is measured transversely with renormalization

Exponential growth of separation on a bounded attractor is compatible with boundedness because the relevant measurement is local transverse stretching with renormalization along the attractor, not unlimited separation in the ambient space.

Conditions: The trajectory lies on an attractor; Separation is measured transversely with renormalization