 ##  [Lyapunov Exponent](/lyapunov-exponent) 

  ##  [Lyapunov Exponent](https://natural.quantumdictionary.io/lyapunov-exponent-0) 

  
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**Natural &amp; Formal Sciences Dictionary**

 
Definition

A real number quantifying the average exponential rate at which nearby trajectories of a dynamical system separate (positive) or converge (negative) along a given direction.

 
 ##  [Lyapunov Exponent](https://mathlogic.quantumdictionary.io/lyapunov-exponent-1) 

  
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- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

A quantitative rate that characterizes the average exponential divergence or convergence of infinitesimally close trajectories in a dynamical system, typically defined as the time-asymptotic limit of the growth rate of small perturbations measured by the logarithm of a tangent map or variational flow.