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                <title xml:lang="en">Joint Spectral Radius, Dilation Equations, and Asymptotic Behavior of Radix-Rational Sequences</title>
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                <term xml:lang="en">Asymptotic analysis Radix-rational sequence Rational formal power series Joint spectral radius Dilation equation Self-similarity</term>
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              <p>Radix-rational sequences are solutions of systems of recurrence equations based on the radix representation of the index. For each radix-rational sequence with complex values we provide an asymptotic expansion, essentially in the scale N^α log^l N. The precision of the asymptotic expansion depends on the joint spectral radius of the linear representation of the sequence of first-order differences. The coefficients are Hölderian functions obtained through some dilation equations, which are usual in the domains of wavelets and refinement schemes. The proofs are ultimately based on elementary linear algebra.</p>
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              <p>Les suites rationnelles dans une base de numération sont solutions de récurrences basées sur la représentation de l'indice dans la base de numération. Pour chacune de ces suites, à valeurs complexes, nous fournissons un développement asymptotique, essentiellement dans l'échelle N^α log^l N. La précision du développement dépend du rayon spectral de la représentation linéaire pour la suite des différences de la suite considérée. Les coefficients sont des fonctions höldériennes obtenues par des équations de dilatation, usuelles dans les théories des ondelettes et des schémas de raffinement. Les preuves sont basées sur l'algèbre linéaire élémentaire.</p>
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