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Transformation of phase space utilizing the Z 2 -symmetry of the dynamical system allows to simplify the phase portrait and at the same time introduces a family of the systems sharing common Lie algebra. We demonstrate application of this transformation to continuous time-space dynamical systems, as well as to their discrete representations on a lattice in the phase space.
Department of Mathematics and Computer Science, Lehman College of the City University of New York, 250 Bedford Park Boulevard West, Bronx, NY 10468, USA