19 citations · 26 across the 14 of their papers we have counts for
18 papers
Purely periodic continued fractions and graph-directed iterated function systems
Giovanni Panti
We describe Gauss-type maps as geometric realizations of certain codes in the monoid of nonnegative matrices in the extended modular group. Each such code, together with an appropr…
Attractors of dual continued fractions
Giovanni Panti
Given a Farey-type map F with full branches in the extended Hecke group Gamma_m, its dual F_# results from constructing the natural extension of F, letting time go backwards, and p…
The finiteness conjecture holds in SL(2,Z>=0)^2
Giovanni Panti, Davide Sclosa
Let A,B be matrices in SL(2,R) having trace greater than or equal to 2. Assume the pair A,B is coherently oriented, that is, can be conjugated to a pair having nonnegative entries.…
Billiards on pythagorean triples and their Minkowski functions
Giovanni Panti
It has long been known that the set of primitive pythagorean triples can be enumerated by descending certain ternary trees. We unify these treatments by considering hyperbolic bill…
Decreasing height along continued fractions
Giovanni Panti
The fact that the euclidean algorithm eventually terminates is pervasive in mathematics. In the language of continued fractions, it can be stated by saying that the orbits of ratio…
Slow continued fractions, transducers, and the Serret theorem
Giovanni Panti
A basic result in the elementary theory of continued fractions says that two real numbers share the same tail in their continued fraction expansions iff they belong to the same orb…