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

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

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
\Bibitem{Dob97} \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 \mathnet{http://mi.mathnet.ru/izv148} \crossref{https://doi.org/10.4213/im148} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1486696} \zmath{https://zbmath.org/?q=an:0896.58049} \transl \jour Izv. Math. \yr 1997 \vol 61 \issue 5 \pages 899--931 \crossref{https://doi.org/10.1070/im1997v061n05ABEH000148} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000071929200001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-21944450763} 

• http://mi.mathnet.ru/eng/izv148
• https://doi.org/10.4213/im148
• http://mi.mathnet.ru/eng/izv/v61/i5/p3

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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
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