*Accepted Paper*

**Inserted:** 24 feb 2017

**Last Updated:** 31 aug 2017

**Journal:** São Paulo Journal of Mathematical Sciences

**Year:** 2017

**Abstract:**

Assume that $W : \mathbb R^m \to \mathbb R$ is a nonnegative potential that vanishes only on a finite set $A$ with at least two elements. By direct minimization of the action functional on a suitable set of maps we give a new elementary proof of the existence of a heteroclinic orbit that connects any given $a_-\in A$ to some $a_+\in A \setminus \{a_- \}$.

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