Characteristic multiplier
Encyclopedia
In mathematics
, and particularly ordinary differential equations, a characteristic multiplier is an eigenvalue of a monodromy matrix
. The logarithm of a characteristic multiplier is also known as characteristic exponent. They appear in Floquet theory of periodic differential operators and in the Frobenius method
.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, and particularly ordinary differential equations, a characteristic multiplier is an eigenvalue of a monodromy matrix
Monodromy matrix
In mathematics, and particularly ordinary differential equations, a monodromy matrix is the inverse of the fundamental matrix of a system of ODEs evaluated at zero times the fundamental matrix evaluated at the period of the coefficients of the system....
. The logarithm of a characteristic multiplier is also known as characteristic exponent. They appear in Floquet theory of periodic differential operators and in the Frobenius method
Frobenius method
In mathematics, the Frobenius method, named after Ferdinand Georg Frobenius, is a way to find an infinite series solution for a second-order ordinary differential equation of the formin the vicinity of the regular singular point z=0....
.
External links
- Examples of finding characteristic multipliers of systems of ODEs from www.exampleproblems.com.