Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable piecewise polynomial vector fields   Consider in R^2 the semi-planes N={y>0} and S={y<0}$ having as common
boundary the straight line D={y=0}$. In N and S are defined polynomial vector
fields X and Y, respectively, leading to a discontinuous piecewise polynomial
vector field Z=(X,Y). This work pursues the stability and the transition
analysis of solutions of Z between N and S, started by Filippov (1988) and
Kozlova (1984) and reformulated by Sotomayor-Teixeira (1995) in terms of the
regularization method. This method consists in analyzing a one parameter family
of continuous vector fields Z_{\epsilon}$, defined by averaging X and Y. This
family approaches Z when the parameter goes to zero. The results of
Sotomayor-Teixeira and Sotomayor-Machado (2002) providing conditions on (X,Y)
for the regularized vector fields to be structurally stable on planar compact
connected regions are extended to discontinuous piecewise polynomial vector
fields on R^2. Pertinent genericity results for vector fields satisfying the
above stability conditions are also extended to the present case. A procedure
for the study of discontinuous piecewise vector fields at infinity through a
compactification is proposed here.

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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph