On a devil's staircase associated to the joint spectral radii of a family of pairs of matrices

DOI10.4171/JEMS/402zbMath1329.15030arXiv1107.3506MaRDI QIDQ363232

Ian D. Morris, Nikita Sidorov

Publication date: 2 September 2013

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.3506

zbMATH Keywords

spectral radiusfamily of matricesSturmian sequence

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Combinatorics on words (68R15) Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Symbolic dynamics (37B10)

Related Items (8)

On the Joint Spectral Radius ⋮ Hourglass alternative and the finiteness conjecture for the spectral characteristics of sets of non-negative matrices ⋮ Spectrum Maximizing Products Are Not Generically Unique ⋮ Continuity properties of the lower spectral radius ⋮ Joint spectral radius, Sturmian measures and the finiteness conjecture ⋮ Ergodic optimization in dynamical systems ⋮ Consensus in asynchronous multiagent systems. II: Method of joint spectral radius ⋮ The joint spectrum

Cites Work

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• The finite-step realizability of the joint spectral radius of a pair of \(d \times d\) matrices one of which being rank-one
• Finiteness property of pairs of \(2\times 2\) sign-matrices via real extremal polytope norms
• Asymptotic height optimization for topical IFS, Tetris heaps, and the finiteness conjecture
• Analysis of the joint spectral radius via lyapunov functions on path-complete graphs
• An Elementary Counterexample to the Finiteness Conjecture

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