18—22.10.2021, Belgrade, Serbia
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Dmitry Serow

Plane Quazicrystals and Four Colours Problem: Trivalent Graph Colouring and Wada Basins


Plane quasicristal geometric structure in connotation Petersen graph colouring has been considered. Petersen graph can represented to be closed electric network (sell) contains $T$ - and $\Delta$-elements. For $Y$ -element volt-ampere characteristic being phase portrait on the plane has been defined. The modelling dynamic system for the $Y$ - element volt-ampere characteristic has been construction. It turns out to be the invariant four regions common boundary.The modelling propagate semi-dynamic system for the plane quasicristal has been constructed. The presence of the Peterson graph colouring and Wada basins have been shown.