Mira, Christian; Carcasses, Jean-Pierre; Millérioux, Gilles; Gardini, Laura Plane foliation of two-dimensional noninvertible maps. (English) Zbl 0879.58063 Int. J. Bifurcation Chaos Appl. Sci. Eng. 6, No. 8, 1439-1462 (1996). 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. Cited in 9 Documents MSC: 37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\) 54C05 Continuous maps Keywords:plane foliation; noninvertible maps; chaotic attractors; basins; bifurcations PDFBibTeX XMLCite \textit{C. Mira} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 6, No. 8, 1439--1462 (1996; Zbl 0879.58063) Full Text: DOI