The results of our research on a family of two dimensional mapping derived from a generalized equation of ∆ ∆-sine Gordon as aforesaid, give us the conclusion; the first trait (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 and the old system each have two fixed point and two point 2-periodic where they can have the type of center (stable) or have type sadle (unstable).
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