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On the asymptotic behaviour of the Lebesgue measure of sum-level sets for continued fractions
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Examples of coarse expanding conformal maps
Continued fractions, Cantor sets, Hausdorff dimension, and transfer operators and their analytic extension
1. | Mathematics Department, Texas A&M University, College Station, TX 77843-3368, United States |
References:
[1] |
V. Baladi and B. Vallée, Euclidean algorithms are Gaussian, J. Num. Th., 110 (2005), 331-386.
doi: 10.1016/j.jnt.2004.08.008. |
[2] |
W. Bosma, H. Jager and F. Wiedijk, Some metrical observations on the approximation by continued fractions, Nederl. Akad. Wetensch. Indag. Math., 45 (1983), 281-299. |
[3] |
J. Bourgain and A. Kontorovich, On Zaremba's Conjecture, C. R. Math. Acad. Sci. Paris, 349 (2011), 493-495. |
[4] |
P. Flajolet and B. Vallée, On the Gauss-Kuzmin-Wirsing constant, unpublished note, 1995. |
[5] |
H. Heilbronn, On the average length of a class of finite continued fractions, in "1969 Number Theory and Analysis (Papers in Honor of Edmund Landau)," Plenum, New York, 87-96. |
[6] |
D. Hensley, The distribution of badly approximable rationals and continuants with bounded digits. II, J. Num. Th., 34 (1990), 293-334.
doi: 10.1016/0022-314X(90)90139-I. |
[7] |
D. Hensley, A polynomial time algorithm for the Hausdorff dimension of continued fraction Cantor sets, J. Num. Th., 58 (1996), 9-45.
doi: 10.1006/jnth.1996.0058. |
[8] |
D. Hensley, The number of steps in the Euclidean algorithm, J. Num. Th., 49 (1994), 142-182.
doi: 10.1006/jnth.1994.1088. |
[9] |
D. Hensley, "Continued Fractions,'' World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2006.
doi: 10.1142/9789812774682. |
[10] |
R. Nair, On metric Diophantine approximation and subsequence ergodic theory, in "New York J. Math.," 3A, (1997/98), Proceedings of the New York Journal of Mathematics Conference, June 9-13, (1997), 117-124. |
[11] |
F. Schweiger, "Multidimensional Continued Fractions," Oxford Science Publications, Oxford University Press, Oxford, 2000. |
[12] |
E. Wirsing, On the theorem of Gauss-Kusmin-Lévy and a Frobenius-type theorem for function spaces, V. Acta Arith., 24 (1973/74), 507-528. |
show all references
References:
[1] |
V. Baladi and B. Vallée, Euclidean algorithms are Gaussian, J. Num. Th., 110 (2005), 331-386.
doi: 10.1016/j.jnt.2004.08.008. |
[2] |
W. Bosma, H. Jager and F. Wiedijk, Some metrical observations on the approximation by continued fractions, Nederl. Akad. Wetensch. Indag. Math., 45 (1983), 281-299. |
[3] |
J. Bourgain and A. Kontorovich, On Zaremba's Conjecture, C. R. Math. Acad. Sci. Paris, 349 (2011), 493-495. |
[4] |
P. Flajolet and B. Vallée, On the Gauss-Kuzmin-Wirsing constant, unpublished note, 1995. |
[5] |
H. Heilbronn, On the average length of a class of finite continued fractions, in "1969 Number Theory and Analysis (Papers in Honor of Edmund Landau)," Plenum, New York, 87-96. |
[6] |
D. Hensley, The distribution of badly approximable rationals and continuants with bounded digits. II, J. Num. Th., 34 (1990), 293-334.
doi: 10.1016/0022-314X(90)90139-I. |
[7] |
D. Hensley, A polynomial time algorithm for the Hausdorff dimension of continued fraction Cantor sets, J. Num. Th., 58 (1996), 9-45.
doi: 10.1006/jnth.1996.0058. |
[8] |
D. Hensley, The number of steps in the Euclidean algorithm, J. Num. Th., 49 (1994), 142-182.
doi: 10.1006/jnth.1994.1088. |
[9] |
D. Hensley, "Continued Fractions,'' World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2006.
doi: 10.1142/9789812774682. |
[10] |
R. Nair, On metric Diophantine approximation and subsequence ergodic theory, in "New York J. Math.," 3A, (1997/98), Proceedings of the New York Journal of Mathematics Conference, June 9-13, (1997), 117-124. |
[11] |
F. Schweiger, "Multidimensional Continued Fractions," Oxford Science Publications, Oxford University Press, Oxford, 2000. |
[12] |
E. Wirsing, On the theorem of Gauss-Kusmin-Lévy and a Frobenius-type theorem for function spaces, V. Acta Arith., 24 (1973/74), 507-528. |
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