Structurally Stable Symmetric Tilings on the Plane

Abstract

A symmetric m-tilings model on the plane is assembled to be a phase portrait for a structurally stable Hamiltonian system. Integral of the system is the quasi-periodic function with m-fold rotational symmetry being result of the semi-dynamic system action on the unit interval. Some examples for pentagonal and heptagonal tilings has been built in detail. Some properties of an additive measure and order for tilings have been discussed.