Bifurcation delay and difference equations

Abstract: We prove the existence of complex analytic solutions of difference equations of the form y(x + ε) = f(x, y(x)), where x, y ∈ CI and ε is a small parameter. We also show that differences of two solutions are exponentially small. We apply these results to the problem of delayed bifurcation at a point of period doubling for real discrete dynamical systems. In contrast to previous publications, the results obtained in this article are global