Abstract
In this paper we present Sarkovskĭ theorem for multidimensional perturbations of one-dimensional maps. We outline a proof that if the unperturbed one-dimensional map has a point of period n, then sufficiently close multidimensional perturbations of this map have periodic points of all periods which are allowed by Sarkovskĭ theorem. We describe also how the approach from the proof of this theorem is used to show the existence of an infinite number of periodic points for Rössler equations.
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