91 citations · 187 across the 14 of their papers we have counts for
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nlin.SI2006★ 17 cited
An integrable hierarchy with a perturbed Henon-Heiles system
A. N. W. Hone, V. S Novikov, C. Verhoeven
We consider an integrable scalar partial differential equation (PDE) that is second order in time. By rewriting it as a system and applying the Wahlquist-Estabrook prolongation alg…
nlin.SI2006★ 24 cited
Singularity confinement for maps with the Laurent property
A. N. W. Hone
The singularity confinement test is very useful for isolating integrable cases of discrete-time dynamical systems, but it does not provide a sufficient criterion for integrability.…
math.NT2006★ 14 cited
Diophantine non-integrability of a third order recurrence with the Laurent property
Andrew Hone
We consider a one-parameter family of third order nonlinear recurrence relations. Each member of this family satisfies the singularity confinement test, has a conserved quantity, a…