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As a model to provide a hands-on, elementary understanding of'vortex dynamics', we introduce a piecewise linear non-invertible map called a twisted baker map. We show that the set of hyperbolic repelling periodic points with complex conjugate eigenvalues and that without complex conjugate eigenvalues are simultaneously dense in the phase space. We also show that these two sets equidistribute with respect to the normalised Lebesgue measure, in spite of a non-uniformity in their Lyapunov exponents.