Analysis of generalized continued fraction algorithms over polynomials

We study and compare natural generalizations of Euclid's algorithm for polynomials with coefficients in a finite field. This leads to gcd algorithms together their associated continued fraction maps. The act on triples rely two-dimensional versions the Brun, Jacobi–Perron fully subtractive maps, respectively. first provide unified framework these then analyse various costs algorithms, including number iterations two bit-complexity, corresponding representations (the usual sparse one). also maps prove invariance ergodicity Haar measure. deduce estimates truncated trajectories under action obtained thanks transfer operators, we models (gcd maps). Proving that generating functions appear as dominant eigenvalues operator allows indeed fine comparison between models.