16 citations · 71 across the 14 of their papers we have counts for
16 papers
Integrable maps in 4D and modified Volterra lattices
A. N. W. Hone, J. A. G. Roberts, P. Vanhaecke +1
In recent work, we presented the construction of a family of difference equations associated with the Stieltjes continued fraction expansion of a certain function on a hyperellipti…
A family of integrable maps associated with the Volterra lattice
A. N. W. Hone, J. A. G. Roberts, P. Vanhaecke
Recently Gubbiotti, Joshi, Tran and Viallet classified birational maps in four dimensions admitting two invariants (first integrals) with a particular degree structure, by consider…
Critical curves of rotations
John A G Roberts, Asaki Saito, Franco Vivaldi
In rotations with a binary symbolic dynamics, a critical curve is the locus of parameters for which the boundaries of the partition that defines the symbolic dynamics are connected…
Critical curves of a piecewise linear map
John A. G. Roberts, Asaki Saito, Franco Vivaldi
We study the parameter space of a family of planar maps, which are linear on each of the right and left half-planes. We consider the set of parameters for which every orbit recurs…
Algebraic entropy of (integrable) lattice equations and their reductions
John A. G. Roberts, Dinh T. Tran
We study the growth of degrees in many autonomous and non-autonomous lattice equations defined by quad rules with corner boundary values, some of which are known to be integrable b…
Linear degree growth in lattice equations
Dinh T Tran, John A G Roberts
We conjecture recurrence relations satisfied by the degrees of some linearizable lattice equations. This helps to prove linear growth of these equations. We then use these recurren…