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On semi-unimodal maps of the plane and the structure of their sets of non-wandering points
V. A. Dobrynskii
We consider a class of semi-unimodal endomorphisms of the plane and study their sets of non-wandering points. It is proved that there are parameter values such that these sets consist of several components, one of which is non-trivially non-compact (that is, has a trajectory receding to infinity), whereas the other components are compact and include a set that is an equivariant image of the Cantor set and part of its boundary is composed of self-similar elements (that is, has a fractal type structure). Furthermore, it turns out that there are parameter values such that the compact and non-compact components intertwine on the coordinate axes.
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Izvestiya: Mathematics, 1997, 61:5, 899–931
V. A. Dobrynskii, “On semi-unimodal maps of the plane and the structure of their sets of non-wandering points”, Izv. RAN. Ser. Mat., 61:5 (1997), 3–34; Izv. Math., 61:5 (1997), 899–931
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\paper On semi-unimodal maps of the plane and the structure of their sets of non-wandering points
\jour Izv. RAN. Ser. Mat.
\jour Izv. Math.
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Bofill F., Garrido J.L., Vilamajo F., Romero N., Rovella A., “On the quadratic endomorphisms of the plane”, Advanced Nonlinear Studies, 4:1 (2004), 37–55
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