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Exact heteroclinic Cycle Family and Quasi-Periodic Solutions for the Three-Dimensional Systems Determined by Chazy Class IX

For differential equation in the Chazy class IX, their corresponding three-dimensional system is studied in this paper by using dynamical system methods and Cosgrove's results. In a level set, the exact explicit parametric representations of a heteroclinic cycle family and uncountably infinitely many periodic solutions as well as quasi-periodic solutions, are all obtained.