Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Markus-Yamabe Conjecture for Differentiable vector fields of R^2   (a) Let X=(f,g) be a differentiable map in the plane (not necessarily C^1)
and let Spec(X) be the set of (complex) eigenvalues of the derivative DX(p)
when p varies in R^2. If, for some \epsilon>0, the set Spec(X) is disjoint of
[0,\epsilon) then X is injective.
  (b) Let X be a differentiable vector field such that X(0)=0 and $Re(z)< 0$
for all z in Spec(X). Then, for all p in R^2, there is a unique positive
trajectory starting at p; moreover the \omega-limit set of p is equal to {0}.

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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex