Papers

Here is a list of my publications. (Updated December 2017)

26. Exceptional digit frequencies and expansions in non-integer bases, 29 pages, submitted.

25. Numbers with simply normal β-expansions, 28 pages, submitted (with D. Kong).

24. Bifurcation sets arising from non-integer base expansions, 22 pages, submitted (with P. Allaart and D. Kong).

23. Digit frequencies and self-affine sets with non-empty interior, 44 pages, submitted.

22. Root sets of polynomials and power series with finite choices of coefficients (with H. Yu), 6 pages, Computational Methods and Function theory (to appear)

21. An analogue of Khintchine’s theorem for self-conformal sets, 26 pages, submitted.

20. Entropy, Topological transitivity, and Dimensional properties of unique q-expansions (with R. Alcaraz Barrera and D. Kong), 56 pages, Transactions of the American Mathematical Society (to appear).

19. On periodic representations in non-Pisot bases (with Z. Masáková, E. Pelantová, and T. Vávra), 14 pages, Monatshefte für Mathematik (to appear).

18. Unique expansions and intersections of Cantor sets (with D. Kong), 19 pages, Nonlinearity (to appear).

17. On the regularity of the generalised golden ratio function (with W. Steiner), 11 pages, Bulletin of the London Mathematical Society (to appear).

16. Induced Random β-transformation (with K. Dajani), 11 pages, Acta Arithmetica (to appear).

15. Inhomogeneous self-similar sets with overlaps (with J. Fraser and A. Mathe), 15 pages, Ergodic Theory and Dynamical Systems (to appear).

14. Approximation properties of β-expansions II, 16 pages. Ergodic Theory and Dynamical Systems (to appear).

13. On small bases for which 1 has countably many expansions (with Y. Zou, L. Wang, and J. Lu), Mathematika 62(2) (2016), 362-377.

12. Dynamical properties of S-gap shifts and other shift spaces (with A. Ghenciu), J. Math. Anal. Appl. 430 (2015), no. 2, 633-647.

11. On the distribution of powers of real numbers modulo 1, Uniform Distribution Theory, 10 (2015), no. 2, 65-73.

10. Approximation properties of β-expansions, Acta Arithmetica, 168 (2015), 269–287.

9. On univoque points for self-similar sets (with K. Dajani and K. Jiang), Fund. Math. 228 (2015), 265-282.

8. Badly approximable numbers for sequences of balls, not for submission, we later found that the work undertaken previously appeared in a paper of Cassels.

7. On the cardinality and complexity of the set of codings for self-similar sets with positive Lebesgue measure, Monatsh. Math. 179(1) (2016), 1-13.

6. On small bases which admit countably many expansions, Journal of Number Theory 147 (2015), 515-532.

5. Expansions in non-integer bases: lower order revisited (with N. Sidorov), Integers 14 (2014), Paper No. A57.

4. On universal and periodic β-expansions, and the Hausdorff dimension of the set of all expansions, Acta Mathematica Hungarica, Volume 142, Issue 1 (2014), Page 95-109.

3. Generalised golden ratios over integer alphabets, Integers 14 (2014), Paper No. A15.

2. The growth rate and dimension theory of beta-expansions, Fund. Math. 219 (2012), 271-285.

1. A multifractal zeta function for cookie cutter sets, Nonlinearity 26 (2013) 1125-1142.

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