What we've discussed our research results about a family of two-dimensional mapping derived from a generalized equation of ∆ ∆-sine Gordon give our conclusion: the first properties (integrable mapping, measure preserving mapping, reversible mapping, andsymmetry 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 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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