Concepedia

Multidimensional Continued Fractions

Multidimensional Continued Fractions is a mathematical framework that generalizes classical continued fractions to higher dimensions by approximating vectors of real numbers through iterative lattice basis reductions, thereby enabling simultaneous rational approximation in multiple variables.

50

Publications

1.2K

Citations

81

Authors

68

Institutions

Publications per year

2017–2026

12

Parents

Publications

50

The modular symbol and continued fractions in higher dimensions

Avner Ash, Lee Rudolph · Inventiones mathematicae · 1979 · 99 citations

, , +10

On the fractional dimension of sets of continued fractions

Tomasz Łuczak · Mathematika · 1997 · 77 citations

, , +11

Geodesic Multidimensional Continued Fractions

Jeffrey C. Lagarias · Proceedings of the London Mathematical Society · 1994 · 68 citations

, , +12

Multidimensional Continued Fractions, Dynamical Renormalization and KAM Theory

Kostya Khanin, João Lopes Dias, Jens Marklof · Communications in Mathematical Physics · 2006 · 54 citations · Full text

, , +12

Scheidegger's rivers, Takayasu's aggregates and continued fractions

Greg Huber · Physica A Statistical Mechanics and its Applications · 1991 · 53 citations · Full text

, , +7

1–5 of 50

Authors

81

  1. RD
    Roman Dmytryshyn

    Vasyl Stefanyk Carpathian National University, Ukraine

    7 publications · 136 citations

    7

    h-index

  2. VB
    Valérie Berthé

    Centre National de la Recherche Scientifique, France

    3 publications · 56 citations

    3

    h-index

  3. DІ
    D. І. Bodnar

    West Ukrainian National University, Ukraine

    3 publications · 44 citations

    3

    h-index

  4. AN
    Arnaldo Nogueira

    Universidade Federal do Rio de Janeiro, Brazil

    3 publications · 59 citations

    3

    h-index

  5. ON
    Oleg N. German

    Lomonosov Moscow State University, Russia

    3 publications · 54 citations

    3

    h-index

1–5 of 81

Institutions

68

  1. Vasyl Stefanyk Carpathian National University

    Ivano-Frankivsk, Ukraine

    7 h-index

    9 publications

    172 citations

  2. Centre National de la Recherche Scientifique

    Paris, France

    5 h-index

    7 publications

    140 citations

  3. West Ukrainian National University

    Ternopil, Ukraine

    3 h-index

    3 publications

    44 citations

  4. Universidade Federal do Rio de Janeiro

    Rio de Janeiro, Brazil

    2 h-index

    2 publications

    49 citations

  5. University of Akron

    Akron, United States

    2 h-index

    2 publications

    29 citations

  6. Williams College

    Williamstown, United States

    2 h-index

    6 publications

    102 citations

  7. The University of Texas at Austin

    Austin, United States

    2 h-index

    3 publications

    39 citations

  8. Université de Montpellier

    Montpellier, France

    2 h-index

    2 publications

    60 citations

1–8 of 68

Venues

  1. Ergodic Theory and Dynamical Systems

    7 publications · 133 citations

    7

    h-index

  2. Carpathian Mathematical Publications

    5 publications · 80 citations

    5

    h-index

  3. Matematychni Studii

    2 publications · 38 citations

    2

    h-index

  4. Communications in Mathematical Physics

    2 publications · 79 citations

    2

    h-index

  5. Sbornik Mathematics

    2 publications · 39 citations

    2

    h-index

1–5