Resonance Sequences and Focal Decompositions

Resumen:

Resonance sequences appeared Geometric Theory of Ordinary Differential equations as an invariant of the linear equations of the second order under the focal equivalence. It is defined as follows. Let A = {a_1,.... a_k} be a nite multiset of positive real numbers. Consider the sequence of all positive integers multiples of all a_i , and note the multiplicity of each term in this sequence. This sequence of multiplicities is called the resonance sequence generated by  {a_1.... a_k}.

We are going to show the relations with focal decompositions and show some properties of the resonances sequences.

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