Pure Mathematics Research
Main areas of research activity are algebra, including group theory, semigroup theory, lattice theory, and computational group theory, and analysis, including fractal geometry, multifractal analysis, complex dynamical systems, Kleinian groups, and diophantine approximations.
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Recent Submissions

Threedimensional forceddamped dynamical systems with rich dynamics : bifurcations, chaos and unbounded solutions
(2015)  Journal articleWe consider certain autonomous threedimensional dynamical systems that can arise in mechanical and fluiddynamical contexts. Extending a previous study in Craik and Okamoto (2002), to include linear forcing and damping, ... 
Recurrence and transience for suspension flows
(2015)  Journal articleWe study the thermodynamic formalism for suspension flows over countable Markov shifts with roof functions not necessarily bounded away from zero. We establish conditions to ensure the existence and uniqueness of equilibrium ... 
A note on the probability of generating alternating or symmetric groups
(201509)  Journal articleWe improve on recent estimates for the probability of generating the alternating and symmetric groups An and Sn. In particular, we find the sharp lower bound if the probability is given by a quadratic in n−1. This leads ... 
Lengths of words in transformation semigroups generated by digraphs
(20160808)  Journal articleGiven a simple digraph D on n vertices (with n≥2), there is a natural construction of a semigroup of transformations ⟨D⟩. For any edge (a, b) of D, let a→b be the idempotent of rank n−1 mapping a to b and fixing all vertices ... 
Idempotent rank in the endomorphism monoid of a nonuniform partition
(201602)  Journal articleWe calculate the rank and idempotent rank of the semigroup E(X,P) generated by the idempotents of the semigroup T(X,P), which consists of all transformations of the finite set X preserving a nonuniform partition P. We ...