Geodesic
On periodic approximate solutions of dynamical systems with a quadratic right-hand side
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIII, Tome 507 (2021), pp. 157-172 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider difference schemes for dynamical systems $ \dot x = f (x) $ with a quadratic right-hand side that have $t$-symmetry and are reversible. Reversibility is interpreted in the sense that the Cremona transformation is performed at each step of 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, values are found for the step $ \Delta t $ for which the approximate solution is a sequence of points with period $ n \in \mathbb N $. Examples are given, and conjectures about the structure of the sets of initial data generating sequences with period $ n $ are formulated. 
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A. Baddour; M. D. Malykh; L. A. Sevastianov. On periodic approximate solutions of dynamical systems with a quadratic right-hand side. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIII, Tome 507 (2021), pp. 157-172. http://geodesic.mathdoc.fr/item/ZNSL_2021_507_a8/

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