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Robust normal forms for saddles of analytic vector fields

The aim of this paper is to introduce a technique for describing trajectories of systems of ordinary differential equations (ODEs) passing near saddle-fixed points. In contrast to classical linearization techniques, the methods of this paper allow for perturbations of the underlying vector fields. This robustness is vital when modelling systems containing small uncertainties, and in the development of numerical ODE solvers producing rigorous error bounds.