Dynamic Symmetries at the Critical Point

A new class of dynamic symmetries is introduced. It is suggested that an element of this class, associated with zeros of Bessel functions, be used to describe spectra of nuclei at or around the critical point of the $\mathrm{U}\left(5\right)-\mathrm{SO}\left(6\right)$ shape phase transition, and, in general, spectra of systems undergoing a (second order) phase transition between the algebraic structures $\mathrm{U}(n-1\mathrm{})$ and $\mathrm{SO}\left(n\right)$.