On a new continued fraction expansion with non-decreasing partial quotients

Monatshefte fur Mathematik

Volumn 143, Issue 4, 2004, Pages 285-298

  Kraaikamp, Cor ^a,c   Wu, Jun ^b  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b WUHAN UNIVERSITY   (China)

^c WESLEYAN UNIVERSITY   (United States)

Author keywords

Engel continued fraction expansion; Hausdorff dimension; Metric property

Indexed keywords

EID: 11944262950     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00605-004-0246-3     Document Type: Article

References (16)

1. Dajani K, Kraaikamp C (2002) Ergodic Theory of Numbers. Washington, DC: Math Assoc America
2. Erdös P, Rényi A, Szüsz P (1958) On Engel's and Sylvester's series. Ann Sci Budapest, Sectio Math 1: 7-32
3. Pisano L, Sigler LE (2002) Fibonacci's Liber abaci. Sources and Studies in the History of Mathematics and Physical Sciences. New York: Springer
4. Galambos J (1970) The ergodic properties of the denominators in the Oppenheim expansion of real numbers into infinite series of rationals. Quart J Math Oxford 21: 177-191
5. Galambos J (1976) Representations of Real Numbers by Infinite Series. Lect Notes Math 502. Berlin Heidelberg New York: Springer
6. Hartono Y, Kraaikamp C, Schweiger F (2002) Algebraic and ergodic properties of a new continued fraction algorithm with non-decreasing partial quotients. J Théor Nombres Bordeaux 14: 497-516
7. Khintchine AYa (1935) Metrische Kettenbruchprobleme. Compositio Math 1: 361-382
8. Lévy P (1929) Sur le loi de probabilité dont dependent les quotients complets et incomplets d'une fraction continue. Bull Soc Math de France 57: 178-194
9. Liu YY, Wu J (2001) Hausdorff dimensions in Engel expansions. Acta Arith 99: 79-83
10. Rényi A (1962) A new approach to the theory of Engel's series. Ann Univ Sci Budapest, Sectio Math 5: 25-32
11. Schweiger F (1971) Ergodische Theorie der Engelschen und Sylvesterschen Reihen. Czechoslovak Math J 21: 243-245
12. Schweiger F (1995) Ergodic Theory of Fibred Systems and Metric Number Theory. Clarendon Press: Oxford
13. Schweiger F (2004) Continued fractions with increasing digits. Öster Akad Wiss, Mathem-Naturw Kl Sitzungsber Abt. II (to appear)
14. Sierpiński W (1974) Sur quelques algorithmes pour développer les nombres réel en séries. In: Oeuvres choisies Tome I, pp 236-254. Warszawa: PWN
15. Thaler M (1979) Maximilian σ-endliche invariante Masse für die Engelschen Reihen. Anz Österreich Akad Wiss, Math-Natur Kl 116: 46-48
16. Wu J (2000) A problem of Galambos on Engel expansions. Acta Arith 92: 383-386