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Izv. RAN. Ser. Mat., 1997, Volume 61, Issue 5, Pages 3–34 (Mi izv148)  

This article is cited in 1 scientific paper (total in 1 paper)

On semi-unimodal maps of the plane and the structure of their sets of non-wandering points

V. A. Dobrynskii


Abstract: 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.

DOI: https://doi.org/10.4213/im148

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English version:
Izvestiya: Mathematics, 1997, 61:5, 899–931

Bibliographic databases:

MSC: 58F15
Received: 13.11.1995

Citation: 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

Citation in format AMSBIB
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\by V.~A.~Dobrynskii
\paper On semi-unimodal maps of the plane and the structure of their sets of non-wandering points
\jour Izv. RAN. Ser. Mat.
\yr 1997
\vol 61
\issue 5
\pages 3--34
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\transl
\jour Izv. Math.
\yr 1997
\vol 61
\issue 5
\pages 899--931
\crossref{https://doi.org/10.1070/im1997v061n05ABEH000148}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  crossref  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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