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We present a Lohner-type algorithm for rigorous integration of systems ofDelay Differential Equations (DDEs) with multiple delays and its application incomputation of Poincar\'e maps to study the dynamics of some bounded, eternalsolutions. The algorithm is based on a piecewise Taylor representation of thesolutions in the phase-space and it exploits the smoothing of solutionsoccurring in DDEs to produces enclosures of solutions of a high order. We applythe topological techniques to prove various kinds of dynamical behavior, forexample, existence of (apparently) unstable periodic orbits in Mackey-GlassEquation (in the regime of parameters where chaos is numerically observed) andpersistence of symbolic dynamics in a delay-perturbed chaotic ODE (theR\"ossler system).

High-order Lohner-type algorithm for rigorous computation of Poincar\'e maps in systems of Delay Differential Equations with several delays