The results of our research on a family of two dimensional mapping derived from a generalized equation of ∆ ∆-sine Gordon give our conclusion, the first traits (integrable mapping, measure preserving mapping, mapping, and a reversible symmetry mapping) on the original mapping having done the Exchange parameter μ that exists in the system and that is in the integralnya give the same properties. This means the original system did not experience a change of nature after the exchanged parameters; And the second, the new system has two fixed points and two 2-point with the same name which they can type center (stable) or sadle (unstable).
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