# The dynamics of Pythagorean Triples

@inproceedings{Romik2004TheDO, title={The dynamics of Pythagorean Triples}, author={Dan Romik}, year={2004} }

We construct a piecewise onto 3-to-1 dynamical system on the positive quadrant of the unit circle, such that for rational points (which correspond to normalized Primitive Pythagorean Triples), the associated ternary expansion is finite and is equal to the address of the PPT on Barning's (1963) ternary tree of PPTs, while irrational points have infinite expansions. The dynamical system is conjugate to a modified Euclidean algorithm. The invariant measure is identified, and the system is shown to… CONTINUE READING

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