### Planar nonautonomous polynomial equations III. Zeros of the vector field

#### Abstract

We give a few sufficient conditions for the existence of periodic solutions

of the equation $\dot{z}=\sum_{j=0}^n a_j(t)z^j$. We prove the existence

of one up to $n$ periodic solutions and heteroclinic ones.

of the equation $\dot{z}=\sum_{j=0}^n a_j(t)z^j$. We prove the existence

of one up to $n$ periodic solutions and heteroclinic ones.

#### Keywords

eriodic solutions; isolating segments

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