Abstract
Some ordinary differential equations have the remarkable property that their Euler’s discretization is chaotic with any fixed time step. It will be shown that discretization of symmetric O.D.E. doesn’t have any periodic orbit with periodn which is greater than 2. This means that chaos requires an asymmetric property in some sense. Moreover, we will show that the existence of 2-periodic orbit and its stability.
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Maeda, Y. Euler’s discretization of ordinary differential equation with symmetric nonlinearity. Japan J. Indust. Appl. Math. 15, 1–6 (1998). https://doi.org/10.1007/BF03167394
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DOI: https://doi.org/10.1007/BF03167394