Lyapunov-Schmidt reduction for periodic orbits of implicit discrete dynamical systems

We derive bifurcation equations for periodic orbits of autonomous and periodically non-autonomous implicit discrete systems in arbitrary finite dimension. Cyclic Lyapunov--Schmidt reduction gives recursive coefficients and nondegeneracy and transversality conditions at the multipliers +1 and -1. We prove equivalence under regular changes of implicit representation and exact invariance under cyclic relabelling when the reduction data are transported consistently.