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Plane foliation of two-dimensional noninvertible maps. (English) Zbl 0879.58063

Summary: The plane foliation consists in associating a sheet with each determination of the inverse map. Such sheets join by pairs at curves called “critical curves”, locus of points having two coincident rank-one preimages. The knowledge of the foliation, i.e., the sheets organization, is of first importance for understanding the properties of noninvertible maps, in particular those of chaotic attractors, basins, and their bifurcations.

MSC:

37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)
54C05 Continuous maps
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