Abstract

In this paper we study the projective vector field Q T of a three-dimensional quasi-homogeneous system with weight ( 1 , 1 , α 3 ) and degree δ = 2 , α 3 ≥ 2 . Projective vector fields Q T of this kind are classified into two types. For one type, Q T has no closed orbit and at most eight singularities, which lead to a global topology of the three-dimensional system. For the other type, Q T has at most ten singularities. In addition, we show a relationship between Q T and a Lienard system of this type. For both of them we obtain some conditions for the existence of limit cycles.

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