Please use this identifier to cite or link to this item:
|Type:||Artigo de periódico|
|Title:||Global Injectivity Of C1 Maps Of The Real Plane, Inseparable Leaves And The Palais-smale Condition|
|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.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.