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We study the exponentially small splitting of separatrices in an analyticone-parameter family of area-preserving maps that generically unfolds a 1:3resonance. Near the resonance the normal form theory predicts existence of asmall triangle formed by separatrices of a period three hyperbolic point. Weprove that in a generic family the separatrices split, provided that the Stokesconstant of the map does not vanish. This constant describes the distancebetween the analytical continuations of invariant manifolds associated with thedegenerate saddle of the map at the exact resonance. We provide an asymptoticformula which describes the size of the splitting. The leading term of thisasymptotic formula is proportional to the Stokes constant.

Splitting of separatrices in a family of area-preserving maps that unfolds a fixed point at the resonance of order three