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Quasi-attractors in a Piece-Wise Smooth Area-Preserving Map

In a two-dimensional area-preserving map we found a kind of noninvertibility that is induced by a piece-wise smooth property of the map. This can lead to the appearance of such kinds of elliptic islands that attract the iterations from a set of initial values outside themselves, while behaving regularly inside. We suggest calling such islands quasi-attractors. PACS: 05. 45. -a