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
Area-Preserving (Hamiltonian), the product of
Eigenvalues is 1.
See also Adiabatic Invariant, Chaos, Lyapunov Characteristic Exponent
© 1996-9 Eric W. Weisstein
1999-05-25