Shadowing in a neighborhood of a separatrix (Q2251819)

The author analyzes certain type of diffeomorphisms of the plane into itself possessing two hyperbolic fixed points joined by a separatrix. It is proven that, under additional assumptions, there is an \(\varepsilon>0\) such that for every \(\delta>0\), there is a special finite \(\delta\)-pseudo-orbit that is not \(\varepsilon\)-shadowed by any point in the plane. Another technical condition is given under which a pseudotrajectory from a special region of space is shadowed by some point in the plane.