Pré-Publication, Document De Travail Année : 2025

ANALYTICITY OF THE PRESSURE FUNCTION FOR PRODUCTS OF MATRICES

Résumé

The pressure function is a fundamental object in various areas of mathematics. Its regularity is studied to derive insights into phase transitions in certain physical systems or to determine the Hausdorff dimension of self-affine sets. In this paper, we prove the analyticity of the pressure function for products of non-invertible matrices satisfying an irreducibility and a contractivity assumptions. Additionally, we establish a variational principle for the pressure function, thereby generalizing previous results.

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Dates et versions

hal-04892297 , version 1 (16-01-2025)

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  • HAL Id : hal-04892297 , version 1

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Arnaud Hautecoeur. ANALYTICITY OF THE PRESSURE FUNCTION FOR PRODUCTS OF MATRICES. 2025. ⟨hal-04892297⟩
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