CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  Publicationsjournals
Publications        
Search results

Search: MSC category 34H05 ( Control problems [See also 49J15, 49K15, 93C15] )

  Expand all        Collapse all Results 1 - 1 of 1

1. CMB 2007 (vol 50 pp. 377)

Gutierrez, C.; Jarque, X.; Llibre, J.; Teixeira, M. A.
Global Injectivity of $C^1$ Maps of the Real Plane, Inseparable Leaves and the Palais--Smale Condition
We study two sufficient conditions that imply global injectivity for a $C^1$ map $X\colon \R^2\to \R^2$ such that its Jacobian at any point of $\R^2$ 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 $X$.

Categories:34C35, 34H05

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/