On Periodic Approximate Solutions of Dynamical Systems with Quadratic Right-Hand Side

Difference schemes are considered for dynamical systems ẋ = f(x) with a quadratic right-hand side, which have t-symmetry and are reversible. Reversibility is interpreted in the sense that the Cremona transformation is performed at each step in the calculations using a difference scheme. The inheritance of periodicity and the Painlevé property by the approximate solution is investigated. In the computer algebra system Sage, such values are found for the step ∆t, for which the approximate solution is a sequence of points with the period n ∈ N. Examples are given and hypotheses about the structure of the sets of initial data generating sequences with the period n are formulated.

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