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On local diffeomorphisms ofR n that are injective

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There are obtained conditions under which maps fromR n to itself are globally injective. In particular there are proved some partial results related to the Weak Markus-Yamabe Conjecture which states that if a vector field X:R nR n has the property that, for allpR n, all the eigenvalues ofD X (p) have negative real part, thenX has at most one singularity.

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Correspondence to Alexandre Fernandes.

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Dedicated to Jorge Sotomayor on his 60th birthday

Part of this work was supported by the CNPq and by PRONEX/FINEP/MCT Grant # 66.2249/1997–6. Teoria Qualitativa das Equações Diferenciais Ordinárias

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Fernandes, A., Gutierrez, C. & Rabanal, R. On local diffeomorphisms ofR n that are injective. Qual. Th. Dyn. Syst 4, 255 (2004).

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Key Words

  • Global injectivity
  • Jacobian Conjecture
  • Weak Markus-Yamabe Conjecture