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Izvestiya: Mathematics, 1997, Volume 61, Issue 5, Pages 899–931
DOI: https://doi.org/10.1070/im1997v061n05ABEH000148 (Mi im148) 		 
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
English version PDF (586 kB) Citations (1)
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DOI: https://doi.org/10.1070/im1997v061n05ABEH000148
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.
Received: 13.11.1995
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 1997, Volume 61, Issue 5, Pages 3–34
DOI: https://doi.org/10.4213/im148
Bibliographic databases:
MSC: 58F15
Language: English
Original paper language: Russian
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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\paper On semi-unimodal maps of the plane and the structure of their sets of non-wandering points
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\yr 1997
\vol 61
\issue 5
\pages 3--34
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\transl
\jour Izv. Math.
\yr 1997
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\pages 899--931
\crossref{https://doi.org/10.1070/im1997v061n05ABEH000148}
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  • https://doi.org/10.1070/im1997v061n05ABEH000148
  • https://www.mathnet.ru/eng/im/v61/i5/p3
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:309
    Russian version PDF:177
    English version PDF:10
    References:49
    First page:1
     
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