Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/104615
Type: Artigo de periódico
Title: Global Injectivity Of C1 Maps Of The Real Plane, Inseparable Leaves And The Palais-smale Condition
Author: Gutierrez C.
Jarque X.
Llibre J.
Teixeira M.A.
Abstract: We study two sufficient conditions that imply global injectivity for a C1 map X: ℝ2 → ℝ2 such that its Jacobian at any point of ℝ2 is not zero. One is based on the notion of half-Reeb component and the other on the Palais-Smale condition. We improve the first condition using the notion of inseparable leaves. We provide a new proof of the sufficiency of the second condition. We prove that both conditions are not equivalent, more precisely we show that the Palais-Smale condition implies the nonexistence of inseparable leaves, but the converse is not true. Finally, we show that the Palais-Smale condition it is not a necessary condition for the global injectivity of the map X. © Canadian Mathematical Society 2007.
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Address: http://www.scopus.com/inward/record.url?eid=2-s2.0-34548598149&partnerID=40&md5=959551d17f203c5f79ef9b6d8ad4deec
Date Issue: 2007
Appears in Collections:Unicamp - Artigos e Outros Documentos

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