Asymptotic height optimization for topical IFS, Tetris heaps, and the finiteness conjecture

By Thierry Bousch, J. Mairesse. 2001

183 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6dc6882cdfe12e69c36a207f5c3aba78592f8d54

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

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Citations in the corpus

Structure of extremal trajectories of discrete linear systems and the finiteness conjecture (2007, methodology): “Then, in the same manner as in [11, 12], with the use of the technique of the Gram symbols borrowed from [ 5 ], we investigate the structure of the so-called “switching sets” of Barabanov norms playing the principal role in description of the properties of extremal trajectories.”
The generalized spectral radius and extremal norms (2002, background): “It has recently been shown by Bousch and Mairesse [ 21 ], that this conjecture is false.”
Finiteness property of pairs of 2× 2 sign-matrices via real extremal polytope norms (2010, background): “) Although it was conjectured to be valid in all cases (see [21]), the finiteness property does not hold for every finite family (see [7], [3], [18]) but has been conjectured to be true for some classes of matrices.”
Mather sets for sequences of matrices and applications to the study of joint spectral radii (2011, methodology): “Mairesse [13], but continues to stimulate research [7, 14, 25, 30, 33, 38].”
On the finiteness property for rational matrices (2007, result): “This conjecture, known as the finiteness conjecture, has attracted intense attention in recent years and has been proved to be false by several authors [4, 7, 12].”
Corrigendum/addendum to: Sets of matrices all infinite products of which converge (2001, unknown): “A preprint of Bousch and Mairesse [6] announces a disproof of the finiteness conjecture.”
ERGODIC OPTIMIZATION OF BIRKHOFF AVERAGES AND LYAPUNOV EXPONENTS (2017, methodology): “The Lyapunov maximizing measures for the one-step cocycles in the examples from [17, 55] (among others) are Sturmian and so have linear complexity.”
Continuity properties of the lower spectral radius (2013, methodology): “It is closely related to the Mañé lemma used by T. Bousch and J. Mairesse in [BM’02] to study both the upper and the lower spectral radii of sets of matrices satisfying a positivity condition (see also [Bou’00, Lemme A] for a related result) and to the concave ‘antinorm’ used by N. Guglielmi and V”