Continued fractions
Continued Fractions and Dynamics
... The connection between Number Theory and Dynamical Systems Theory is receiving recently a considerable attention. In this paper, we review some aspects of this connection focusing on the interplay between ...
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On examples of two-dimensional periodic continued fractions
... The interest for multidimensional continued fractions was revived by V. I. Arnold’s work [1]. He realized the reasons of Klein’s failure and proposed a new approach to the study of the multidimensional ...
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Continued fractions which correspond to two series expansions and the strong Hamburger moment problem
... The significance of finding such corresponding continued fractions was only realised when Frobenius and Pad~ arrived at general and elaborate techniques of obtaining rational approximant[r] ...
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Identification of Patterns of Continued Fractions of √s – [√s] Where is a Square Free Positive Number
... Continued fractions provide much insight into mathematical problems, particularly into the nature of numbers ...to continued fractions is found in the works of the Indian mathematician ...
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Contents. 6 Continued Fractions and Diophantine Equations. 6.1 Linear Diophantine Equations
... We begin by analyzing a few simple Diophantine equations, then discuss the ideas behind rational approximation and develop the theory of continued fractions.. Finally, we apply these res[r] ...
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Generalized continued fractions: a unified definition and a Pringsheim type convergence criterion
... of continued fractions found in the ...non-generalized continued fractions, a Worpitzky-type criterion by means of equivalence transformation), that is, all results mentioned in ...
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Modular relations and explicit values of Ramanujan Selberg continued fractions
... By employing a method of parameterizations for Ramanujan’s theta-functions, we find several modular relations and explicit values of the Ramanujan-Selberg continued fractions.. Copyright[r] ...
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An Efficient PRBG Based on Chaotic Map and Engel Continued Fractions
... pendent initial conditions. The pseudo random bit se- quence is generated by comparing the outputs of both the chaotic standard maps. They presented the detailed re- sults of the statistical testing on generated bit ...
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Convergence of Vectorial Continued Fractions Related to the Spectral Seminorm
... Theorem 2.5 below gives a necessary condition for convergence according to the spectral seminorm. This result is an extension of von Koch Theorem 4, concerning the scalar case. A similar theorem was given by Fair 1 for ...
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Continued Fractions of Ratios of Consecutive Polygonal Numbers
... In this paper we try to find some patterns of ratios of consecutive polygonal numbers of different sides and different orders using continued fractions... Proof: Similar to the proof of[r] ...
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Probabilities as Values of Modular Forms and Continued Fractions
... continued fraction. However, one may generalize these two cases, thanks to Theorem 1.2, by making use of the so-called Selberg relations 6 see also 7 which extend the notion of a continued fraction. Arguing ...
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Open problems in geometry of continued fractions
... multidimensional continued fractions One of the main source of problems in this area are the problems of face structure description of sails and the corresponding ...
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Continued fractions and class number two
... both continued fractions and ...with continued fractions, we first note that it is well known that a real number has a periodic continued fraction expansion if and only if it is a ...
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On a theorem of Serret on continued fractions
... in continued fractions due to Ser- ret shows that for any two irrational numbers x and y related by a transformation γ in PGL(2, Z ) there exist s and t for which the complete quotients x s and y t ...
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Applications of Continued Fractions in Cryptography and Diophantine Equations
... of continued fractions has applications in cryptographic problems and in so- lution methods for Diophantine ...of continued fractions such as convergents and approximations to real ...on ...
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Block Matrix Representation of a Graph Manifold Linking Matrix Using Continued Fractions
... In this article, we consider the following question: how the topological invariants of manifold corresponding to a tree graph graph manifold can be calculated using the method of Gauss-N[r] ...
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On Raney's binary encoding for continued fractions, generalisations of Pell's Equation, and the theory of factorisation
... arc concerned with the formulation and justification of Raney's algorithm for the solution of the folloreing problem: Given a real nunber x as a continued fraction, anC integers a.brcrd,[r] ...
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Analysis of Complex Continued Fractions of The Solution of The Equation kx2-nx+n=0 Where n is An Odd Integer And k=[n/2]
... fraction, Periodic complex continued fraction, Gaussian integer, Euclidean algorithm, Quadratic irrational.. KRITHIKA.[r] ...
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A brief interaction with continued fractions
... Not only does t he probability density f * = Inh l ~x represent t he invariant density function of the G-K-\V operator , it is also the "time" averaged probability density of t he orbit[r] ...
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FACTORING WITH CONTINUED FRACTIONS, THE PELL EQUATION, AND WEIGHTED MEDIANTS
... the continued fraction expan- sion of √ N is too short, then the algorithm can only produce a small factor basis, which reduces the chances for factoring N ...
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