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AiA2 Applying the Painleve arbitrary coefficients bosonic sector branch the coefficients Brasil Brasileiro de Pesquisas Centro Brasileiro chaotic Cny2 considered covariant derivatives degrees of freedom dimensional reduction Dirac dominant potencies dominant terms E-mail fermionic interactions following compatibility condition following potential fourth order gauge potentials gauge theories Grassmannian Henon-Heiles potential impose parity symmetry integrable cases found kinetic terms l.M l.M Lyapunov exponent mechanical system non-integrable potential NOTAS DE FÍSICA obtain four branches Painleve property Painleve test parameters parity invariance particular ansatz pass the Painleve pass the test Pesquisas Físicas phase portraits phase space potentials above preserve Publicações Rua Dr replace the truncated Rio de Janeiro role of parity role of supersymmetry second branch show integer resonances firstname.lastname@example.orgemail@example.com http://www.biblioteca.cbpf.br/index_2.html solutions spatially homogeneous field spinor superfield coordinates superpotential superspace supersymmetric mechanical supersymmetry and parity system passes transform under parity Ui(t Uj,o Uj,r verified x3 and y4 Xavier Sigaud y-parity Yang-Mills theory