Branquinho, A.Moreno, A. FoulquiéMendes, A.2025-10-152025-10-152016-11-11Branquinho, A., Foulquié Moreno, A., & Mendes, A. (2016). Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials. Integral Transforms and Special Functions, 28(1), 74–90. https://doi.org/10.1080/10652469.2016.12500821065-24691476-8291http://hdl.handle.net/10400.8/14266In this work we characterize a high-order Toda lattice in terms of a family of matrix polynomials orthogonal with respect to a com plex matrix measure. In order to study the solution of this dynamical system, we give explicit expressions for the Weyl function, general ized Markov function, and we also obtain, under some conditions, a representation of the vector of linear functionals associated with this system. We show that the orthogonality is embedded in these structure and governs the high-order Toda lattice. We also present a Lax-type theorem for the point spectrum of the Jacobi operator associated with a Toda-type lattice.engMatrix orthogonal polynomialsLinear functionalRecurrence relationOperator theoryMatrix Sylvester differential equationsToda-type systemsLax-type theoremjournal article10.1080/10652469.2016.1250082