Articolele autorului Dan Lascu
Link la profilul stiintific al lui Dan Lascu

A Gauss-Kuzmin-type problem for a family of continued fraction expansions

In this paper we study in detail a family of continued fraction expansions of any number in the unit closed interval [0,1] whose digits are differences of consecutive non-positive integer powers of an integer m⩾2. For the transformation which generates this expansion and its invariant measure, the Perron–Frobenius operator is given and studied. For this expansion, we apply the method of random systems with complete connections by Iosifescu and

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Properties of the Lehner continued fractions expansions
Solving a Gauss – Kuzmin Theorem for RCF using RSCC
Nonhyperbolic singularities of Bogdanov – Takens type in an epidemic model
Random systems with complete connections and the Gauss problem for the regular continued fractions
A new type of continued fraction expansion
On the Szüsz’s solution to Gauss’ problem
Properties of the nearest integer continued fraction expansions
Jump transformations and embedding of O_∞ into O_2
Continued Fraction Expansions and Permutative Representations of the Cuntz Algebra O_∞

We show a correspondence between simple continued fraction expansions of irrational numbers and irreducible permutative representations of the Cuntz algebra O_∞. In regard to the correspondence, it is shown that the equivalence of real numbers with respect to modular transformations is equivalent to the unitary equivalence of representations. Furthermore, we show that quadratic irrationals are related to irreducible permutative representations

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