caa a22 4500 477118453 CHVBK 20180405111629.0 cr unu---uuuuu 170330e19960401xx s 000 0 eng 10.1007/BF02259526 doi (NATIONALLICENCE)springer-10.1007/BF02259526 Exponentially small splitting of separatrices for difference equations with small step size [Elektronische Daten] [A. Fruchard, R. Schäfke] Solutions of the vector difference equationy(x+ε)−y(x−ε)=2εf(x,y(x)),x being a complex variable and ε>0 a small parameter, are constructed that are analytic onx-domains Ω which are independent of ε. As the first case, horizontally convex bounded domains are considered, i.e., domains having the property that for eachx, x′∈Ω with the same imaginary part, the interval [x, x′] is contained in Ω; also considered are unbounded domains such as sectors open on the left or on the right. Using these results, it is shown that the Hausdorff distance between separatrices of certain systems of difference equations is exponentially small with respect to ε. As an application, the so-called ghost solutions of the discretized logistic equation are considered in detail and, in particular, the lengths of the levels are estimated. Other applications, e.g., to the standard mapping, are presented. Plenum Publishing Corporation, 1996 Difference equation nationallicence singular perturbation nationallicence ghost solution nationallicence invariant manifold nationallicence Fruchard A. Institut de Recherche Mathématique Avancée U.F.R. de Mathématiques et Informatique, Université Louis Pasteur et C.N.R.S., 7, rue René Descartes, 67084, Strasbourg CEDEX, France aut Schäfke R. Institut de Recherche Mathématique Avancée U.F.R. de Mathématiques et Informatique, Université Louis Pasteur et C.N.R.S., 7, rue René Descartes, 67084, Strasbourg CEDEX, France aut Journal of Dynamical and Control Systems Kluwer Academic Publishers-Plenum Publishers 2/2(1996-04-01), 193-238 1079-2724 2:2<193 1996 2 10883 https://doi.org/10.1007/BF02259526 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02259526 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Fruchard A. Institut de Recherche Mathématique Avancée U.F.R. de Mathématiques et Informatique, Université Louis Pasteur et C.N.R.S., 7, rue René Descartes, 67084, Strasbourg CEDEX, France aut NATIONALLICENCE 700 1- Schäfke R. Institut de Recherche Mathématique Avancée U.F.R. de Mathématiques et Informatique, Université Louis Pasteur et C.N.R.S., 7, rue René Descartes, 67084, Strasbourg CEDEX, France aut NATIONALLICENCE 773 0- Journal of Dynamical and Control Systems Kluwer Academic Publishers-Plenum Publishers 2/2(1996-04-01), 193-238 1079-2724 2:2<193 1996 2 10883 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer