Abstract :
For a class of reversible quadratic vector fields on R3 we study the periodic orbits that bifurcate from
a heteroclinic loop having two singular points at infinity connected by an invariant straight line in the finite
part and another straight line at infinity in the local chart U2. More specifically, we prove that for all n ∈ N,
there exists εn > 0 such that the reversible quadratic polynomial differential system
˙x = a0 +a1y + a3y2 +a4y2 +ε a2x2 +a3xz ,
˙y = b1z +b3yz +εb2xy,
˙z = c1y +c4z2 +εc2xz
in R3, with a0 < 0, b1c1 < 0, a2 < 0, b2 < a2, a4 > 0, c2 < a2 and b3 /∈ {c4, 4c4}, for ε ∈ (0, εn) has at
least n periodic orbits near the heteroclinic loop.
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