  Lorentz invariance violation (LIV) is a proposed phenomenon where Lorentz
symmetry is violated at high energies, potentially affecting particle dynamics
and interactions. We use numerical simulations with the CRPropa framework to
investigate LIV in gamma-ray-induced electromagnetic cascades, specifically
studying how it impacts cascading electrons and photons undergoing pair
production and inverse Compton scattering. Our detailed analysis of the
simulation results, compared with existing theoretical models, reveals that LIV
can significantly alter the behavior of both components of the cascade, photons
and electrons, resulting in specific signatures in measured fluxes that could
be observed in high-energy gamma-ray observations. These insights are crucial
for ongoing searches for LIV and for the development of theoretical models
incorporating LIV effects.
