Abstract
The closeness of the approximate ( P L ) and the exact ( P ) Poincaré mappings for ODE systems with a hyperbolic critical point possessing a homoclinic orbit, is studied. The mappings are shown to be not uniformly close in their whole domain. The existence of the uniform estimate in a general case is provided by the restriction of mappings P , P L to some subset. The images of mappings P L and P occur to be uniformly close in the whole domain only for particular cases of 2-dimensional systems, systems with a single unstable direction at the equilibrium point and systems with two unstable directions corresponding to a complex conjugate pair of eigenvalues.
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