  Non-Hermitian systems and their topological singularities, such as
exceptional points (EPs), lines, and surfaces, have recently attracted intense
interest. The investigation of these exceptional constituents has led to
fruitful applications. The responsivity of the eigenvalue diverges at EPs, and
chiral state transfer occurs when encircling an EP. Traditionally, it was
believed that these exceptional features were unique to non-Hermitian systems
requiring gain, loss, or nonreciprocal hopping. Here, we show that these
exceptional features are also present in nonlinear Hermitian systems. We
consider two coupled resonators with Kerr nonlinearity in one resonator, and no
non-Hermitian terms. We identify EP-like points (ELPs) on the eigenspectra
where the critical behaviors are the same as those of typical EPs.
Additionally, this nonlinear Hermitian system can be mapped to linear
non-Hermitian systems, with ELPs corresponding to EPs. We also demonstrate that
encirclement around an ELP in the parameter space leads to unique chiral state
transfer behavior.
