  Band structures of metamaterials described by a nonlinear eigenvalue problem
are beyond the existing topological band theory. In this paper, we analyze
non-Hermitian topology under the nonlinearity of eigenvalues. Specifically, we
elucidate that such nonlinear systems may exhibit exceptional points and
non-Hermitian skin effects which are unique non-Hermitian topological
phenomena. The robustness of these non-Hermitian phenomena is clarified by
introducing the topological invariants under nonlinearity which reproduce the
existing ones in linear systems. Furthermore, our analysis elucidates that
exceptional points may emerge even for systems without an internal degree of
freedom where the equation is single component. These nonlinearity-induced
exceptional points are observed in mechanical metamaterials, e.g., the Kapitza
pendulum.
