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pro vyhledávání: '"Panti, Giovanni"'
Autor:
Panti, Giovanni
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 appropriate choice of unimodular intervals in P^1R, determines a dual pair of
Externí odkaz:
http://arxiv.org/abs/2307.16658
Autor:
Panti, Giovanni
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 projecting. Although numerical simulations may suggest otherwise, we sh
Externí odkaz:
http://arxiv.org/abs/2105.13237
Autor:
Panti, Giovanni, Sclosa, Davide
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. Assume also that either A,B^(-1) is coherently oriented as well, or A
Externí odkaz:
http://arxiv.org/abs/2006.16899
Autor:
Panti, Giovanni
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 billiard tables in the Poincare disk model. Our tables have m>=3 ideal ver
Externí odkaz:
http://arxiv.org/abs/1902.00414
Akademický článek
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Autor:
Panti, Giovanni
Publikováno v:
Ergod. Th. Dynam. Sys. 40 (2020) 763-788
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 rational points under the Gauss map x-->{1/x} eventually reach zero. Analog
Externí odkaz:
http://arxiv.org/abs/1802.09378
Autor:
Panti, Giovanni
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 orbit under the projective action of PGL(2,Z). This result was first form
Externí odkaz:
http://arxiv.org/abs/1706.00698
Autor:
Panti, Giovanni
The Farey sequence is the sequence of all rational numbers in the real unit interval, stratified by increasing denominators. A classical result by Hall says that its normalized gap distribution is the same as the distribution of the random variable 1
Externí odkaz:
http://arxiv.org/abs/1503.02539
Autor:
Panti, Giovanni, Ravotti, Davide
The half-open real unit interval (0,1] is closed under the ordinary multiplication and its residuum. The corresponding infinite-valued propositional logic has as its equivalent algebraic semantics the equational class of cancellative hoops. Fixing a
Externí odkaz:
http://arxiv.org/abs/1203.2513