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We introduce and study the linear symmetric systems associated with the modified Cherednik operators. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite propagation speed property of it. Les systèmes symétriques linéaires associés aux opérateurs de Cherednik modifiés et applications Résumé Nous présentons et étudions les systèmes symétriques linéaires associés aux opérateurs de Cherednik modifiés. Nous prouvons que le problème de Cauchy pour ces systèmes sont bien posé. Finalement nous en décrivons le principe de vitesse finie. Dedicated to Khalifa Trimèche for his 66th birthday

The linear symmetric systems associated with the modified Cherednik operators and applications