Lyapunov Exponents for Matrices with Invariant Subspaces
Key, Eric S.
Ann. Probab., Tome 16 (1988) no. 4, p. 1721-1728 / Harvested from Project Euclid
If $\mathbf{M}$ is a fixed $d \times d$ complex-valued matrix, then the eigenvalues of $\mathbf{M}'$, the conjugate transpose of $\mathbf{M}$, are the complex conjugates of the eigenvalues of $\mathbf{M}$, with the same multiplicities, and if $\mathbf{M}$ is upper block triangular, the eigenvalues of $\mathbf{M}$ are the eigenvalues of the diagonal blocks, and the multiplicities add. We shall show that if $\{\mathbf{M}(j)\}$ is a stationary, ergodic, time-reversible sequence taking values in the $d \times d$ complex matrices, then similar properties hold for the Lyapunov exponents of $\{\mathbf{M}(j)\}$.
Publié le : 1988-10-14
Classification:  Lyapunov exponents,  Oseledec's multiplicative ergodic theorem,  invariant subspaces,  60B15,  60H25
@article{1176991593,
     author = {Key, Eric S.},
     title = {Lyapunov Exponents for Matrices with Invariant Subspaces},
     journal = {Ann. Probab.},
     volume = {16},
     number = {4},
     year = {1988},
     pages = { 1721-1728},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991593}
}
Key, Eric S. Lyapunov Exponents for Matrices with Invariant Subspaces. Ann. Probab., Tome 16 (1988) no. 4, pp.  1721-1728. http://gdmltest.u-ga.fr/item/1176991593/