The distributions of limit cycles of cubic vector fields (P2, Q3) are considered in this paper, where P2 and Q3 are polynomials of x and y of order two and three, respectively. It is possibly seven different distributions of limit cycles given in [1]. We now prove that in which three kinds of distributions are impossible and other four kinds all can be realized by concrete vector fields of (P2,Q3). Some related results are also given.
Let X be a metric space. We say that a continuous surjection f:X→X is a topological Anosov map (abbrev. TA map) if f is expansive and has pseudo orbit tracing property with respect to some compatible metric for X . This paper studies the properties of TA maps of non compact metric spaces and gives some conditions for the map to be topologically mixing.
