In
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, and particularly
ordinary differential equations
In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives ...
, a characteristic multiplier is an
eigenvalue
In linear algebra, an eigenvector ( ) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector \mathbf v of a linear transformation T is scaled by a ...
of a
monodromy matrix. The logarithm of a characteristic multiplier is also known as characteristic exponent.
They appear in
Floquet theory
Floquet theory is a branch of the theory of ordinary differential equations relating to the class of solutions to periodic linear differential equations of the form
:\dot = A(t) x,
with x\in and \displaystyle A(t) \in being a piecewise continu ...
of periodic differential operators and in the
Frobenius method
In mathematics, the method of Frobenius, named after Ferdinand Georg Frobenius, is a way to find an infinite series solution for a linear second-order ordinary differential equation of the form
z^2 u'' + p(z)z u'+ q(z) u = 0
with u' \equiv \frac a ...
.
See also
*
Multiplier (disambiguation)
References
{{reflist
External links
Examplesof finding characteristic multipliers of systems of ODEs from www.exampleproblems.com.
Ordinary differential equations