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商洛学院数学与计算机应用学院初等数论课件Chapter 5 Continued Fractions
商洛学院数学与计算机应用学院 初等数论 课件 Chapter 5 Continued Fractions
2017/4/7
商洛学院数学与计算机应用学院初等数论课件Chapter 5 Continued Fractions.
We establish new combinatorial transcendence criteria for continued fraction expansions. Let α = [0; a1, a2, . . .] be an algebraic number of degree at least three. One of our criteria implies that th...
Dynamics of continued fractions and kneading sequences of unimodal maps
Dynamics of continued fractions kneading sequences of unimodal maps
2011/1/20
The goal of this paper is to provide a link between the parameter spaces of two families of one-dimensional dynamical systems, and to shed some light onto some sets of numbers which arise as “exceptio...
Natural extensions and entropy of $\alpha$-continued fractions
Natural extensions entropy
2010/11/23
We construct a natural extension for each of Nakada's $\alpha$-continued fractions and show the continuity as a function of $\alpha$ of both the entropy and the measure of the natural extension domai...
A note on the l´evy constant for continued fractions
Continued fractions l´ evy constant Hausdorff dimension
2010/2/25
In this note, we study the l´evy constant of continued fraction expansions. We show that for all x ∈ [0, 1),
the upper l´evy constant of x is finite except a set with Hausdorff dimension ...
We find a generating function expressed as a continued fraction that enumerates ordered trees by the number of vertices at different levels. Several Catalan problems are mapped to an ordered-tree pro...