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The operator $\Lambda_{\{2\},\{3\}}$ acting on line arrangements is definedby associating to a line arrangement \mathcal{A}, the line arrangement which isthe union of the lines containing exactly three points among the double pointsof \mathcal{A}. We say that six lines not tangent to a conic form an unassumingarrangement if the singularities of their union are only double points, but thedual line arrangement has six triple points, six 5-points and 27 double points.The moduli space of unassuming arrangements is the union of a point and a line.The image by the operator $\Lambda_{\{2\},\{3\}}$ of an unassuming arrangementis again an unassuming arrangement. We study the dynamics of the operator$\Lambda_{\{2\},\{3\}}$ on these arrangements and we obtain that the periodicarrangements are related to the Ceva arrangements of lines.

On the dynamics of the line operator $\Lambda_{\{2\},\{3\}}$ on some arrangements of six lines