Difference between revisions of "Monodromy matrix"
From Encyclopedia of Mathematics
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| − | A constant | + | {{TEX|done}} |
| + | A constant $(n\times n)$-matrix $X(\omega)$ which is the value at $t=\omega$ of the [[Fundamental matrix|fundamental matrix]] $X(t)$, normalized at zero, of a linear system of differential equations | ||
| − | + | $$\dot x=A(t)x,\quad t\in\mathbf R,\quad x\in\mathbf R^n,$$ | |
| − | with an | + | with an $\omega$-periodic matrix $A(t)$ that is summable on each compact interval in $\mathbf R$. |
Latest revision as of 17:01, 12 August 2014
A constant $(n\times n)$-matrix $X(\omega)$ which is the value at $t=\omega$ of the fundamental matrix $X(t)$, normalized at zero, of a linear system of differential equations
$$\dot x=A(t)x,\quad t\in\mathbf R,\quad x\in\mathbf R^n,$$
with an $\omega$-periodic matrix $A(t)$ that is summable on each compact interval in $\mathbf R$.
Comments
References
| [a1] | J.K. Hale, "Ordinary differential equations" , Wiley (1969) |
How to Cite This Entry:
Monodromy matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Monodromy_matrix&oldid=16847
Monodromy matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Monodromy_matrix&oldid=16847
This article was adapted from an original article by Yu.V. Komlenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article