Dynamical dimensional reduction in multivalued Hamiltonians

Several interesting physical systems, such as the Lovelock extension of general relativity in higher dimensions, classical time crystals, $k$-essence fields, Horndeski theories, compressible fluids, and nonlinear electrodynamics, have apparent ill-defined sympletic structures, due to fact that their Hamiltonians are multivalued functions momenta. In this paper, dynamical evolution generated by is described a degenerate system, whose form does not constant rank, allowing novel features interpretations present previous investigations. particular, it shown how multivaluedness associated with mechanism dimensional reduction, some degrees freedom turn into gauge symmetries when system degenerates.