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| This paper aims at providing an example of a family of polynomial Li\'{e}nard equations exhibiting
an alien limit cycle. This limit cycle is perturbed from a $2$-saddle cycle in the boundary of an annulus of
periodic orbits given by a Hamiltonian vector field. The Hamiltonian represents a truncated pendulum of degree $4$. In comparison to a former polynomial example, not only the equations are simpler but a lot of tedious calculations can be avoided, making the example also interesting with respect to simplicity in treatment. |
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