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Generalized continued fractions and ergodic theory
Journal of Mathematical Sciences, 1999A standard theory of one-dimensional continued fractions is based on the sequential application of the so-called Gauss map and the comparison of the result to zero. The author proposes a generalization of this procedure to the case when one uses some other map, say \(A\), and an arbitrary stopping rule (e.g., the comparison to a given value \(\omega ...
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Generalizing the continued fraction algorithm to arbitrary dimensions
30th Annual Symposium on Foundations of Computer Science, 1989A new \(N\)-dimensional continued fraction algorithm is presented. Its most remarkable property is that it produces infinitely many solutions of the diophantine inequality \(\max_{1\leq i\leq N}| x_ i q-p_ i|\ll q^{-w(N)}\) with \(w(N)=1/2N(N+1)\). It also detects linear dependence.
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Convergence of generalized continued fractions
International Journal of Computer Mathematics, 1982A general theory for the convergence of Generalized Continued Fractions, based on an inclusion property of complex regions, is given. Due to the appearance of divisions of complex regions, the theory cannot be applied in the general case. This is even so for the case of complex discs, but for these special regions the theory can be adjusted in order to
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Generalized continued fractions associated with the Gauss transform
Russian Mathematical Surveys, 2002In this short note the author describes some properties of the so-called \(\omega\)-continued fractions \(x=[a_0,a_1,\dots]_\omega\), which are a one-dimensional variant of the multidimensional \((A,\omega)\)-continued fractions, which was introduced by the author in [Math. Notes 56, No. 6, 1315--1317 (1994); translation from Mat. Zametki 56, No.
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Other Generalizations of Continued Fractions
Algorithms and Computation in Mathematics, 2022Oleg N Karpenkov
exaly
Combinatorial properties of multidimensional continued fractions
Discrete Mathematics, 2023Giordano Santilli +2 more
exaly
Generalized Notions of Continued Fractions
2023Juan Fernández Sánchez +3 more
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Two generalizations of Ramanujan's continued fraction identities
Lecture Notes in Mathematics, 1985Chandrashekar Adiga
exaly