  We consider a mechanical lattice inspired by the Su-Schrieffer-Heeger model
along with cubic Klein-Gordon type nonlinearity. We investigate the long-time
dynamics of the nonlinear edge states, which are obtained by nonlinear
continuation of topological edge states of the linearized model. Linearly
unstable edge states delocalize and lead to chaos and thermalization of the
lattice. Linearly stable edge states also reach the same fate, but after a
critical strength of perturbation is added to the initial edge state. We show
that the thermalized lattice in all these cases shows an effective
renormalization of the dispersion relation. Intriguingly, this renormalized
dispersion relation displays a unique symmetry, i.e., its square is symmetric
about a finite squared frequency, akin to the chiral symmetry of the linearized
model.
