Bifurcation delay and difference equations.

Augustin Fruchard (1) , Reinhard Schäfke (2)

1 LMIA - Laboratoire de Mathématiques Informatique et Applications [UHA]
2 IRMA - Institut de Recherche Mathématique Avancée

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.

Mots clés: bifurcation delay; difference equation; dynamical system; discrete canard

Domaines: Analyse classique [math.CA]

Augustin Fruchard, Reinhard Schäfke. Bifurcation delay and difference equations.. Nonlinearity, 2003, 16 (6), pp.2199-2220. ⟨hal-00144872⟩