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Wave modes in periodic systems of thin tubes

The problem of wave propagation in a periodic system of thin tubes is studied. The waves are described by the dispersion diagrams, i.e. by the dependencies of the propagation constants on the temporal frequency. The main question under consideration is how many modes can propagate in a particular system. The paper presents a method of finding the dispersion diagrams, and an inequality for the number of modes, linking the number of modes with the topological properties of the system.