Asymptotically exact spectral estimates for left triangular matrices

Details Asymptotically exact spectral estimates for left triangular matrices Asymptotically exact spectral estimates for left triangular matrices

2000-09-08

arxiv.org/abs/nlin/0009020v1

Nonlinear Sciences

Chaotic Dynamics

7 pages, LaTeX

Scientific paper

For a family of $n*n$ left triangular matrices with binary entries we derive asymptotically exact (as $n\to\infty$) representation for the complete eigenvalues-eigenvectors problem. In particular we show that the dependence of all eigenvalues on $n$ is asymptotically linear for large $n$. A similar result is obtained for more general (with specially scaled entries) left triangular matrices as well. As an application we study ergodic properties of a family of chaotic maps.

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