A remark on linear differential systems with the same invariant subbundles
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- by Robert E. Vinograd PDF
- Proc. Amer. Math. Soc. 86 (1982), 305-306 Request permission
Abstract:
Given a flow $\sigma (\omega ,t) = \omega \cdot t$ on a compact metric space $\Omega$ and a continuous $n \times n$-matrix $A(\omega )$, the family of ODE systems $\dot x = A(\omega \cdot t)x$ defines a linear skew-product flow on $W = \Omega \times X$, $X = {R^n}$ or ${C^n}$. Let $W = U \oplus V$ be a Whitney sum and $P:W \to W$ be the correspondent projector. Result: the subbundles $U$ and $V$ are invariant for the flows induced by $A(\omega )$ and $B(\omega )$ iff $A(\omega )$-$B(\omega )$ commutes with $P(\omega )$ for all $\omega \in \Omega$.References
- Robert J. Sacker and George R. Sell, A spectral theory for linear differential systems, J. Differential Equations 27 (1978), no. 3, 320–358. MR 501182, DOI 10.1016/0022-0396(78)90057-8
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 305-306
- MSC: Primary 58F25
- DOI: https://doi.org/10.1090/S0002-9939-1982-0667294-8
- MathSciNet review: 667294