Related papers: The random continued fraction transformation
An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous…
Our aim is to find a complex continued fraction algorithm finding all the best Diophantine approximations to a complex number. Using the sequence of minimal vectors in a two dimensional lattice over Gaussian integers, we obtain an algorithm…
Two approximations, derived from continuous expansions of Riemann-Liouville fractional derivatives into series involving integer order derivatives, are studied. Using those series, one can formally transform any problem that contains…
The goal of this paper is to formulate a systematical method for constructing the fastest possible continued fraction approximations of a class of functions. The main tools are the multiple-correction method, the generalized Mortici's lemma…
Proper continued fractions are generalized continued fractions with positive integer numerators $a_i$ and integer denominators with $b_i\geq a_i$. In this paper we study the strength of approximation of irrational numbers to their…
We consider a family $\{\tau_m:m\geq 2\}$ of interval maps introduced by Hei-Chi Chan [5] as generalizations of the Gauss transformation. For the continued fraction expansion arising from $\tau_m$, we solve its Gauss-Kuzmin-type problem by…
We introduce a variant of the replica trick within the nonlinear sigma model that allows calculating the distribution function of the persistent current. In the diffusive regime, a Gaussian distribution is derived. This result holds in the…
We generalize the exact solution to the Bernoulli shift map. Under certain conditions, the generalized functions can produce unpredictable dynamics. We use the properties of the generalized functions to show that certain dynamical systems…
In this paper the computational aspects of probability calculations for dynamical partial sum expressions are discussed. Such dynamical partial sum expressions have many important applications, and examples are provided in the fields of…
We give a new algorithm of slow continued fraction expansion related to any real cubic number field as a 2-dimensional version of the Farey map. Using our algorithm, we can find the generators of dual substitutions (so-called tiling…
We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum in terms of solutions to Vlasov-type hierarchies. As a by-product we obtain the evolution of the density of particles in the…
Using the slow triangle map (a type of multi-dimensional continued fraction algorithm), we exhibit a method for generating any number of new identities for subsets of integer partitions.
An extension of Riewe's fractional Hamiltonian formulation is presented for fractional constrained systems. The conditions of consistency of the set of constraints with equations of motion are investigated. Three examples of fractional…
We extend the Series' connection between the modular surface $\mathcal{M}=\operatorname{PSL}(2,\mathbb{Z})\backslash\mathbb{H}$, cutting sequences, and regular continued fractions to the slow converging Lehner and Farey continued fractions…
The Hankel transform of an integer sequence is a much studied and much applied mathematical operation. In this note, we extend the notion in a natural way to sequences of $d$ integer sequences. We explore links to generalized continued…
Within the study of uncertain dynamical systems, iterated random functions are a key tool. There, one samples a family of functions according to a stationary distribution. Here, we introduce an extension, where one sample functions…
By applying the MC algorithm and the Bauer-Muir transformation for continued fractions, in this paper we shall give six examples to show how to establish an infinite set of continued fraction formulas for certain Ramanujan-type series, such…
This paper studies the chance constrained fractional programming with a random benchmark. We assume that the random variables on the numerator follow the Gaussian distribution, and the random variables on the denominator and the benchmark…
We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and…
Fast Fourier transforms are used to develop algorithms for the fast generation of correlated Gaussian random fields on d-dimensional rectangular regions. The complexities of the algorithms are derived, simulation results and error analysis…