Homepage for Karma Dajani
Department of Mathematics P.O. Box 80.010 3508 TA Utrecht The Netherlands e-mail: k.dajani1@uu.nl tel: +31-30-253-1424 fax: +31-30-251-8394  directions

I am a senior lecturer and researcher at the University of Utrecht. My research interests are primarily in ergodic theory and its application to other fields such as number theory, probability theory and symbolic dynamics. See also my publications.

I am also interested in the area of financial mathematics and I have been the master thesis advisor of several students who wrote their thesis in this area.

Information on courses I am giving at the university college UCU

Information on courses I am giving at the Bachelors level.

Information on course I am giving at the Masters level.

Information on the course I am giving at Würzburg University

Information on the course I am giving for Mastermath and SFM 2014

Information on the course Brownian Motion and Financial Mathematics2015-16

Information on the course Brownian Motion and Financial Mathematics2016-17

• Dajani, K. Genericity of nontrivial $H$-superrecurrent $H$-cocycles. Trans. Amer. Math. Soc. 323 (1991), no. 1, 111--132.
• Dajani, K. On superrecurrence. Canad. Math. Bull. 34(1991), no. 1, 48--57.
• Dajani, K. Coboundaries under integrable exponentiation. Tokyo J. Math. 15 (1992), no. 1, 83--89.
• Dajani, K. Generic results for cocycles with values in a semidirect product. Canad. J. Math. 45 (1993), no. 3, 497--516.
• Dajani, K., Hawkins and J. Rohlin factors, product factors, and joinings for $n$-to-one maps. Indiana Univ. Math. J. 42 (1993), no. 1, 237--258.
• Dajani, K. and Hawkins, J. M. Examples of natural extensions of nonsingular endomorphisms. Proc. Amer. Math. Soc. 120 (1994), no. 4, 1211--1217.
• Dajani, K. and Kraaikamp, C. Generalization of a theorem of Kusmin. Monatsh. Math. 118 (1994), no. 1-2, 55--73.
• Dajani, Karma; Kraaikamp, Cor On approximation by Lüroth series. J. Théor. Nombres Bordeaux 8 (1996), no. 2, 331--346.
• Barrionuevo, J., Burton, R. M., Dajani, K. and Kraaikamp, C. Ergodic properties of generalized Lüroth series. Acta Arith. 74(1996), no. 4, 311--327.
• Dajani, K. and Dooley, A. The mean ratio set for $ax+b$ valued cocycles. Publ. Res. Inst. Math. Sci. 32 (1996), no. 4, 671--688.
• Dajani, K. and Hawkins, J. A construction of a non-measure-preserving endomorphism using quotient relations and automorphic factors. J. Math. Anal. Appl. 204 (1996), no. 3, 854--867.
• Dajani, K., Kraaikamp, C. and Solomyak, B. The natural extension of the ß-transformation. Acta Math. Hungar. 73 (1996), no. 1-2, 97--109.
• Dajani, K. and Kraaikamp, C. A note on the approximation by continued fractions under an extra condition. New York J. Math. 3A (1997/98), Proceedings of the New York Journal of Mathematics Conference, June 9--13, 1997, 69--80 (electronic).
• Burton, R., Dajani, K. and Meester, R. Entropy for random group actions. Ergodic Theory Dynam. Systems 18 (1998), no. 1, 109--124.
• Dajani, Karma; Kraaikamp, Cor A Gauss-Kusmin theorem for optimal continued fractions. Trans. Amer. Math. Soc. 351 (1999), no. 5, 2055--2079.
• Dajani, K. and Kraaikamp, C. "The mother of all continued fractions". Dedicated to the memory of Anzelm Iwanik. Colloq. Math. 84/85 (2000), part 1, 109--123.
• Dajani, K. and Fieldsteel, A. Equipartition of interval partitions and an application to number theory. Proc. Amer. Math. Soc. 129 (2001), no. 12, 3453--3460 (electronic).
• Dajani, K. A note on rotations and interval exchange transformations on 3-intervals. Int. J. Pure Appl. Math. 1 (2002), no. 2, 151--160.
• Dajani, K. and Kraaikamp, Cor From greedy to lazy expansions and their driving dynamics. Expo. Math. 20 (2002), no. 4, 315--327.
• Dajani, K. and Kraaikamp, C. Ergodic theory of numbers. Carus Mathematical Monographs, 29. Mathematical Association of America, Washington, DC, (2002) ISBN: 0-88385-034-6.
• Dajani, K. and Kraaikamp, Cor Random beta-expansions. Ergod. Th. & Dynam. Sys. (2003), 23.
• Dajani, K. and Meester, R. Random Entropy and Recurrence.  International Journal of Mathematics and Mathematical Sciences, vol. 2003 no. 47 (2003), 2977-2988.
• Bezuglyi, S., Dajani, K., Dooley, A.H. and Hamachi , T. Isomorphic actions of group extensions on a measure space. Indag. Math. (N.S.) 15 (2004), no. 2, 167--188.
• Dajani, K. and de Vries, M. Measures of Maximal Entropy for Random beta-expansions.  J. Eur. Math. Soc. (JEMS) 7 (2005), no. 1, 51--68.
• Dajani, K., Properties of expansions to non-integer bases; a survey. CWI Tract 135, (2005), 27--38.
• Dajani, K. and von Reis J., editors of the Proceedings of the 11th conference of EWM, CWI Tract 135 (2005).
• Bosma W., Dajani K. and Kraaikamp C., Entropy quotients and correct digits in number-theoretic expansions.  IMS Lecture Notes-Monograph Series  (Dynamics and Stochastics), vol. 48 (2006).
  

• Dajani, K., Kraaikamp, C., and Liardet, P. Ergodic properties of signed binary expansions,  Disc. and Cont. Dynamical Systems vol. 15, no. 1 (2006).
• Dajani, K., de Vries, M., Johnson A., The relative growth of information in two-dimensional partitions,  Real Analysis Exchange, vol. 31, issue 2 (2006).
• Dajani, K. and de Vries, M. Invariant Densities for Random beta-expansions,   J. Eur. Math. Soc. (JEMS) , vol. 9, issue 1 (2007).
• Dajani, K. and Kalle C. On the convergence of logarithmic first return times, Revue Romaine de Math. Pures et Appl., Volume 52, Number 1, 2007, pp. 35-46.
• Dajani, K. and Kalle C. Random ß-expansions with deleted digits, Discrete and Continuous Dynamical Systems, Volume 18, Number 1, 2007, pp. 199-217.
• Dajani, K., Kraaikamp C., Steiner W. Metrical Properties for alpha-Rosen Continued Fractions.  J. Eur. Math. Soc. (JEMS) 11 (2009), no. 6, 1259--1283.
• Dajani, K., Hartono Y., Kraaikamp C. Mixing Properties of (alpha, beta)-Expansions.  Ergodic Theory Dynam. Systems 29 (2009), no. 4, 1119--1140.
• Dajani, K.; Kalle, C. A natural extension for the greedy $\beta$-transformation with three arbitrary digits. Acta Math. Hungar. 125 (2009), no. 1-2, 21--45.
• Dajani, K. and Kalle C. Natural Extensions for the Golden Mean. Proceedings of the 13th General Meeting of the European Women in Mathematics. World Scientific (2010). ISBN-13 978-981-4277-69-9.
  
• Dajani, K. and Kalle, C. - A note on the greedy beta-transformation with deleted digits. Seminaires et Congres 20 (2010).
• Dajani, Karma; Kalle, Charlene Transformations generating negative β-expansions. Integers 11B (2011), Paper No. A5, 18 pp.
• Dajani K., Komornik V., Loreti P. de Vries M. Optimal expansions in non-integer bases. Proc. Amer. Math. Soc. 140 (2012), no. 2, 437-447.
• Dajani, K.; Ramawadh, S. D. Symbolic dynamics of (−β)-expansions. J. Integer Seq. 15 (2012), no. 2, Article 12.2.6, 21 pp.
• Dajani, K.; Hensley, D.; Kraaikamp, C.; Masarotto, V. Arithmetic and ergodic properties of `flipped' continued fraction algorithms. Acta Arith. 153 (2012), no. 1, 51-79.
• Dajani, Karma; Kraaikamp, Cor; van der Wekken, Niels Ergodicity of N-continued fraction expansions. J. Number Theory 133 (2013), no. 9, 3183-3204.
• Dajani, K.; Kalle, C. Local dimensions for the random β-transformation. New York J. Math. 19 (2013), 285-303.
• Dajani, Karma; Jiang, Kan; Kempton, Tom; Self-affine sets with positive Lebesgue measure. Indag. Math. (N.S.) 25 (2014), no. 4, 774-784.
• Dajani, K., kraaikamp C., Langeveld N., Continued fraction expansions witli variable numerators. Ramanujan J. 37 (2015), no. 3, 617-639.
• Baker, S.; Dajani, K.; Jiang K.;  On univoque points for self-similar sets. Fundamenta Mathematicae 228 (2015), no. 3, 265-282
• Dajani K.; Jiang, K.; Shrinking random beta-expansions. Indag. Math. (N.S.) 28 (2017), no. 1, 74-83.
• Dajani K.; Jiang, K. Subshifts of finite type and self- similar sets. Nonlinearity 30 (2017), no. 2, 659-686.
• Baker, S.; Dajani, K. Induced random beta-transformation. Acta Arith. 178 (2017), no. 1-14.
• Dajani K.;Polman, F. Krijgsman, C.; Hemminga, M. Modelling a Dutch pension fund's capital requirement for Longevity risk; Actuaris Uitgave 24-5 (2017).
• Dajani, K.; Oomen M. Random N-continued fraction expansions. J. Approx. Theory 227 (2018), 1-26.
• Dajani, K.; Komornik, V.; Loreti P. Notes on some of Kahane's works: Ingham type theorem and Bernoulli convolutions; Anal. Math. 44 (2018), no. 2, 207-217.
• Dajani, K. ;Komornik, V.; Kong D.; Li, W. Algebraic sums and products of univoque bases. Indag. Math. (N.S.) 29 (2018), no. 4, 1087-1104.
• Dajani K.; Jiang, K. On points without universal expansions. Acta Arith. 184 (2018), no. 3, 231-245.
• Dajani, K. ;Jiang, K.; Kong D.; Li, W. Multiple expansions of real numbers with digit set {0,1,q}. Math. Z. 291 (2019), no. 3-4, 1605-1619.
• Dajani, K. .; Kong D.; Yao Y. On the structure of lambda-Cantor set with overlaps. Adv. in Appl. Math 108 (2019), 97-125.
• Dajani, K.; de Lepper M.; Robinson E.A. Introducing Minkowski normality. J. Number Theory 211 (2020), 455-476.
• Dajani, K.;Kalle C. Invariant measures, matching and the frequency of 0 for the signed binary expansions. Publ. Res. Inst. Math. Sci. 56 (2020), no. 4, 701-742.
• Dajani, K.; Jiang, K.; Kong D.; Li, W. Multiple codings of self-similar sets with overlaps. Adv. in Appl. Math. 124 (2021), 102-146.
• Dajani, K.;Kalle C; Maggioni M. Matching for random systems with an application to minimal weight expansions. Nonlinearity 34 (2021), no.6, 3676-3708.
• Dajani, K.; Power, K. Equilibrium states for the random beta-transformation via g-measures. Acta Math. Hungar. 166 (2022), no 1, 70-91.
• Cisternino C.; Charlier E.; Dajani K. Dynamical behavior of alternate base expansions. To appear in Ergodic Theory and Dynamical systems.
• Dajani K. Kalle C. A first course in ergodic theory. Chapman and Hall/CRC, 2021 ISBN 9780367226206.
• Dajani K. Langeveld N. Alternating N-expansions. ArXiv 2112.0427v1.
• Dajani K.; Li W.; Zhang Tingyu. Random beta-transformation on fat Sierpinski gasket. ArXiv 2201.07560v1.
  

Last updated: March 14, 2022.