The random continued fraction transformation
نویسندگان
چکیده
منابع مشابه
The Random Continued Fraction Transformation
We introduce a random dynamical system related to continued fraction expansions. It uses random combination of the Gauss map and the Rényi (or backwards) continued fraction map. We explore the continued fraction expansions that this system produces as well as the dynamical properties of the system.
متن کاملcontinued fraction ∗
We use a continued fraction expansion of the sign-function in order to obtain a five dimensional formulation of the overlap lattice Dirac operator. Within this formulation the inverse of the overlap operator can be calculated by a single Krylov space method where nested conjugate gradient procedures are avoided. We show that the five dimensional linear system can be made well conditioned using ...
متن کاملDynamics of a Continued Fraction of Ramanujan with Random Coefficients
We study a generalization of a continued fraction of Ramanujan with random, complexvalued coefficients. A study of the continued fraction is equivalent to an analysis of the convergence of certain stochastic difference equations and the stability of random dynamical systems. We determine the convergence properties of stochastic difference equations and so the divergence of their corresponding c...
متن کاملThe Szekeres Multidimensional Continued Fraction
In his paper "Multidimensional continued fractions" {Ann. Univ. Sei. Budapest. EOtvOs Sect. Math., y. 13, 1970, pp. 113-140), G. Szekeres introduced a new higher dimensional analogue of the ordinary continued fraction expansion of a single real number. The Szekeres algorithm associates with each fc-tuple (a»,..., ak) of real numbers (satisfying 0 < a< 1) a sequence bx, b2,... of positive intege...
متن کاملThe Hurwitz Complex Continued Fraction
The Hurwitz complex continued fraction algorithm generates Gaussian rational approximations to an arbitrary complex number α by way of a sequence (a0, a1, . . .) of Gaussian integers determined by a0 = [α], z0 = α − a0, (where [u] denotes the Gaussian integer nearest u) and for j ≥ 1, aj = [1/zj−1], zj = 1/zj−1−aj . The rational approximations are the finite continued fractions [a0; a1, . . . ,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nonlinearity
سال: 2017
ISSN: 0951-7715,1361-6544
DOI: 10.1088/1361-6544/aa5243