Plot Orbits of Toral Automorphisms

A toral automorphism is a dynamical system defined by a linear map on the torus - that is, the unit square with left and right sides identfied, and the top and bottom identified. See Dynamical Systems on the Torus for an introduction to toral automorphisms. To view the orbit of point (the initial point), enter values below and click Plot orbit.

Enter a 2-by-2 matrix for the linear map defining the toral automorphism.

Enter coordinates of initial point for the orbit.

x:     y:

Number of iterations:

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