A Note on Lyapunov Theory for Brun Algorithm

  • Fritz Schweiger
Part of the Developments in Mathematics book series (DEVM, volume 16)


Regular continued fractions exhibit a number of remarkable properties. We mention three of them.


Metric theory of generalized continued fractions 

2000 Mathematics subject classification

11K55 11J70 


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  1. 1.
    Bernstein, L.: The Jacobi-Perron Algorithm: Its Theory and Application. Lect. Notes Math. 207. Springer, Heidelberg (1971)zbMATHGoogle Scholar
  2. 2.
    Broise-Alamichel, A., Guivarc’h, Y.: Exposants caractéristiques de l’algorithme de Jacobi-Perron et de la transformation associée. Ann. Inst. Fourier 51, 565–686 (2001)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Lagarias, J.C.: The quality of the Diophantine approximations found by the Jacobi-Perron algorithm and related algorithms. Monatsh. Math. 115, 299–328 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Mañé, R.: Ergodic Theory and Differentiate Dynamics. Springer, Heidelberg (1987)Google Scholar
  5. 5.
    Nakaishi, K.: The exponent of convergence for 2-dimensional Jacobi-Perron type algorithms. Monatsh. Math. 132, 141–152 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Schratzberger, B.: The exponent of convergence for Brun’s algorithm in two dimensions. Sitzungsber. Österr. Akad. Wiss. Math.-naturw. Kl. Abt. II207, 229–238 (1998)MathSciNetGoogle Scholar
  7. 7.
    Schweiger, F.: Multidimensional Continued Fractions. Oxford University Press, Oxford (2000)zbMATHGoogle Scholar
  8. 8.
    Schweiger, F.: Diophantine properties of multidimensional continued fractions. In: Dubickas, A., et al. (eds.) Analytic and Probabilistic Methods in Number Theory, pp. 242–255. TEV, Vilnius (2002)Google Scholar
  9. 9.
    Toussaint, H.-J.: Der Algorithmus von Viggo Brun und verwandte Kettenbruchentwicklungen. Dissertation, Technische Universität München, Munich, Germany (1986)Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Fritz Schweiger
    • 1
  1. 1.Department of MathematicsUniversity of SalzburgSalzburgAustria

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