Geodesic
On semi-unimodal maps of the plane and the structure of their sets of non-wandering points
Izvestiya. Mathematics , Tome 61 (1997) no. 5, pp. 899-931

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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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     author = {V. A. Dobrynskii},
     title = {On semi-unimodal maps of the plane and the structure of their sets of non-wandering points},
     journal = {Izvestiya. Mathematics },
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     volume = {61},
     number = {5},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1997_61_5_a0/}
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V. A. Dobrynskii. On semi-unimodal maps of the plane and the structure of their sets of non-wandering points. Izvestiya. Mathematics , Tome 61 (1997) no. 5, pp. 899-931. http://geodesic.mathdoc.fr/item/IM2_1997_61_5_a0/