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

We consider difference schemes for dynamical systems ẋ = f(x) with quadratic right-hand side that have t-symmetry and are reversible. Reversibility is interpreted in the sense that a Cremona transformation is performed at each step of the computations using the difference scheme. The inheritance of periodicity and the Painlevé property by the approximate solution is investigated. In the computer algebra system Sage, values are found for the step Δt for which the approximate solution is a sequence of points with period n ∈ ℕ. Examples are given, and conjectures about the structure of the sets of initial data generating sequences with period n are formulated. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.