We study the energy decay of a network of vibrating elastic strings where the strings are coupled at a common end in a star-shaped configuration. We prove that the solutions are not exponentially stable in the energy space. Moreover, we give explicit polynomial decay estimates valid for regular initial data. These estimates depend on the diophantine approximations properties of the lengths of the strings of the network.
"Stabilization of star-shaped networks of strings." Differential Integral Equations 17 (11-12) 1395 - 1410, 2004.