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Starting from the complete integrable lattice super-KdV equation, twosuper-mappings are obtained by performing a travelling-wave reduction. Thefirst one is linear and the second is a four dimensional super-QRT mappingcontaining both Grassmann commuting and anti-commuting dependent variables.Adapting the classical "staircase" method to the Lax super-matrices of thelattice super-KdV equation, we compute the Lax super-matrices of the mappingand the two invariants; the first one is a pure nilpotent commuting quantityand the second one is given by an elliptic curve containing nilpotent commutingGrassmann coefficients as well. In the case of finitely generated Grassmannalgebra with two generators, the super-QRT mapping becomes a four-dimensionalordinary discrete dynamical system that has two invariants but does not satisfysingularity confinement criterion. It is also observed that the dynamicaldegree of this system grows quadratically.

Super-QRT and 4D-mappings reduced from the lattice super-KdV equation