Given a Lyapunov Characteristic Exponent , the corresponding Lyapunov characteristic number
is defined as

(1) 
For an dimensional linear Map,

(2) 
The Lyapunov characteristic numbers , ..., are the Eigenvalues of the Map
Matrix. For an arbitrary Map

(3) 

(4) 
the Lyapunov numbers are the Eigenvalues of the limit

(5) 
where is the Jacobian

(6) 
If for all , the system is not Chaotic. If
and the Map is
AreaPreserving (Hamiltonian), the product of
Eigenvalues is 1.
See also Adiabatic Invariant, Chaos, Lyapunov Characteristic Exponent
© 19969 Eric W. Weisstein
19990525