Bifurcation delay and difference equations.
Résumé
We prove the existence of complex analytic solutions of difference equations of the form $y(x+eps)=f(x,y(x))$, where x and y are complex variables and $eps$ 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.
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