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

  • Three-dimensional forced-damped dynamical systems with rich dynamics : bifurcations, chaos and unbounded solutions 

    Miyaji, Tomoyuki; Okamoto, Hisashi; Craik, Alexander Duncan Davidson (2015) - Journal article
    We consider certain autonomous three-dimensional dynamical systems that can arise in mechanical and fluid-dynamical contexts. Extending a previous study in Craik and Okamoto (2002), to include linear forcing and damping, ...
  • Recurrence and transience for suspension flows 

    Iommi, Godofredo; Jordan, Thomas; Todd, Michael John (2015) - Journal article
    We 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 

    Morgan, Luke; Roney-Dougal, Colva Mary (2015-09) - Journal article
    We 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 

    Cameron, P. J.; Castillo-Ramirez, A.; Gadouleau, M.; Mitchell, J. D. (2016-08-08) - Journal article
    Given 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 non-uniform partition 

    Dolinka, Igor; East, James; Mitchell, James D. (2016-02) - Journal article
    We 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 non-uniform partition P. We ...

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