Structural Stability of Constrained Polynomial Systems

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. 1991 Mathematics Subject Classification 34C35, 34D30.