Actually, the number of Lyapunov exponents is equal to the number of dimensions of the embedding phase space, but it is common to just refer to the largest one, because it determines the predictability of a dynamical system.
The Lyapunov exponents λi are calculated as
Note however, that phase space volume does not necessarily change over time. If the system is conservative (i.e. there is no dissipation), volume will stay the same.
See also: Lyapunov characteristic number
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The Lyapunov test, also known as the Lyapunov exponent, the methods of approximation by Aleksandr Lyapunov which provide ways of determining the stability of sets of ordinary differential equations (determining the prediction horizon). While there is a whole spectrum of Lyapunov exponents (their number is equal to the dimension of the phase space), the largest is meant; A quantitative measure of the sensitive dependence on the initial conditions; The averaged rate of divergence (or convergence) of two neighboring trajectories; Even qualitative predictions are impossible for a time interval beyond the prediction horizon.
The Lyapunov characteristic exponent [LCE] gives the rate of exponential divergence from perturbed initial conditions.
References (with proper mathematical symbols):