Open
maps: small and large holes with unusual properties (with
K.
G. Hare)
*(version
***October
25, 2017***).*

The
baker's map with a convex hole (with
L.
Clark and K. G. Hare)
*(version
***September
18, 2017***).*

A
lower bound for the dimension of Bernoulli convolutions (with
K.
G. Hare)
*(final
version ***March
1, 2017***),
*to
appear in *Exp.
Math.*

**Recent
papers: **

On
a family of self-affine sets: topology, uniqueness, simultaneous
expansions (with
K.
G. Hare),
*Ergodic
Theory Dynam. Systems*
**37**
(2017),
193-227*.*

Two-dimensional
self-affine sets with interior points, and the set of uniqueness
(with
K.
G. Hare),
*Nonlinearity
***29**
(2016),
1-26.

Multidimensional
self-affine sets: non-empty interior and the set of uniqueness
(with
K.
G. Hare),
*Studia
Math. ***229**
(2015),
223-232.

The
doubling map with asymmetrical holes (with P.
Glendinning),
*Ergodic
Theory Dynam. Systems* **35**
(2015),
1208-1228.

On
cycles for the doubling map which are disjoint from an interval
(with
K.
G. Hare),
*Monatsh.
Math*.
**175**
(2014),
347-365.

Expansions
in non-integer bases: lower order revisited (with S.
Baker),
*Integers
***14**
(2014),
Paper #A57*.*

Supercritical
holes for the doubling map, *Acta
Math. Hung*.
**143**
(2014),
298-312.

Extremal
sequences of polynomial complexity (with
K.
G. Hare and I. D. Morris),
*Math.
Proc. Camb. Phil. Soc*.
**155**
(2013),
191-205.

On
a Devil's staircase associated to the joint spectral radii of a
family of pairs of matrices (with I.
D. Morris),
*J.
Eur. Math. Soc. (JEMS) ***15**
(2013),
1747-1782.

On
the topology of sums in powers of an algebraic number (with B.
Solomyak),
*Acta
Arith.* **149**
(2011),
337-346.

An
explicit counterexample to the Lagarias-Wang finiteness conjecture
(with K.
G. Hare, I. D. Morris and J. Theys),
*Adv.
Math.* **226**
(2011),
4667-4701.

Growth
rate for beta-expansions (with D.-J.
Feng),
*Monatsh.
Math*.
**162**
(2011),
41-60.

**Older
papers:** click
here

Arithmetic
Dynamics, in `Topics
in Dynamics and Ergodic Theory', *LMS
Lecture Notes* *Ser.*
**310
**(2003),
145-189.

Optimizing
Properties of Balanced Words, an extended abstract of my talk for
the 8^{th}
International
Conference WORDS 2011,
*Electr.
Proc. Theoret. Comp. Sci.*
**63**
(2011),
240-246.