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We consider a Kukles system of the form x˙=-y,y˙=f(x,y) where f(x,y) is a polynomial with real coefficients of degree d without y as a divisor. We study the maximum number of small-amplitude limit cycles for these kind of systems which can coexist with invariant algebraic curves.We give all the possible distributions of invariant straight lines for a Kukles system and we give some bounds for the number...
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