Sequências de ressonância e classificação de 3-multiconjuntos sob equivalência combinatória.

Abstract

In this master’s dissertation we study the problem of classification of multisets under combinatorial equivalence. We begin with a short presentation of the focal decomposition of second order differential equations, showing the origins of the resonance sequences. Then, we give some preliminary results, and after that we present the Alvarez Algorithm, together with other results regarding resonance sequences. Finally, we prove the complete criterion of classifi cation of multisets with 3 elements up to combinatorial equivalence, by showing this is equivalent to a system of equations depending directly of the numbers in the multisets.