Asymptotically exact spectral estimates for left triangular matrices

2000/09/08 by Michael Blank, Blank, Michael · 1 citation
Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #nlin.CD

paper · pdf · doi:10.48550/arxiv.nlin/0009020

7 pages, LaTeX

arxiv created 2000/09/08 · openalex publication_date 2000/09/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a family of n*n left triangular matrices with binary entries we derive asymptotically exact (as n→∞) 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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