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STRUCTURAL STABILITY OF CONSTRAINED POLYNOMIAL SYSTEMS

Published online by Cambridge University Press:  01 November 1998

JAUME LLIBRE  and
JORGE SOTOMAYOR
JAUME LLIBRE
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, 08193 Barcelona, Spain
JORGE SOTOMAYOR
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, Agência Cidade de São Paulo, CEP 05389–970, Brazil
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Abstract

The structural stability of constrained polynomial differential systems of the form a(x, y)x′+b(x, y)y′=f(x, y), c(x, y)x′+d(x, y)y′=g(x, y), under small perturbations of the coefficients of the polynomial functions a, b, c, d, f and g is studied. These systems differ from ordinary differential equations at ‘impasse points’ defined by ad−bc=0. Extensions to this case of results for smooth constrained differential systems [7] and for ordinary polynomial differential systems [5] are achieved here.

Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 30 , Issue 6 , November 1998 , pp. 589 - 595
Copyright
© The London Mathematical Society 1998

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