On the Quadratic Endomorphisms of the Plane
Abstract: In this article we establish the following result: if a nondegenerate quadratic endomorphism of the plane has no fixed points, then every point has empty omega-limit set and alpha-limit set. It is also shown that there exists a six parameter family open and dense in the space of all quadratic mappings of the plane (even those having fixed points). The degenerate case (when the quadratic forms of both components are linearly dependent), for which the theorem fails, is considered in the last section.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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On the Quadratic Endomorphisms of the Plane ; volume:4 ; number:1 ; year:2004 ; pages:37-55 ; extent:19
Advanced nonlinear studies ; 4, Heft 1 (2004), 37-55 (gesamt 19)
- Creator
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Bofill, F.
Garrido, J.L.
Vilamajó, F.
Romero, N.
Rovella, A.
- DOI
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10.1515/ans-2004-0103
- URN
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urn:nbn:de:101:1-2405021621131.407132201570
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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14.08.2025, 10:53 AM CEST
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Associated
- Bofill, F.
- Garrido, J.L.
- Vilamajó, F.
- Romero, N.
- Rovella, A.
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