15 citations · 60 across the 7 of their papers we have counts for
10 papers · 1 filter
Complexity and integrability in 4D bi-rational maps with two invariants
G. Gubbiotti, N. Joshi, D. T. Tran +1
In this letter we give fourth-order autonomous recurrence relations with two invariants, whose degree growth is cubic or exponential. These examples contradict the common belief th…
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…
Poisson brackets of mappings obtained as (q,-p) reductions of lattice equations
Dinh T. Tran, Peter H. van der Kamp, G. Reinout W. Quispel
In this paper, we present Poisson brackets of certain classes of mappings obtained as general periodic reductions of integrable lattice equations. The Poisson brackets are derived…
Darboux integrability of determinant and equations for principal minors
Dmitry K. Demskoi, Dinh T. Tran
We consider equations that represent a constancy condition for a 2D Wronskian, mixed Wronskian-Casoratian and 2D Casoratian. These determinantal equations are shown to have the num…
A Lax pair of a lattice equation whose entropy vanishes
Dinh T. Tran
In this paper, we present multi parametric quadgraph equations which are consistent around the cube. These equations are obtained by applying a `double twist' to known integrable e…
Poisson structures for lifts and periodic reductions of integrable lattice equations
Theodoros E. Kouloukas, Dinh T. Tran
We introduce and study suitable Poisson structures for four dimensional maps derived as lifts and specific periodic reductions of integrable lattice equations. These maps are Poiss…
Integrable and superintegrable systems associated with multi-sums of products
Peter H. van der Kamp, Theodoros E. Kouloukas, G. R. W. Quispel +2
We construct and study certain Liouville integrable, superintegrable, and non-commutative integrable systems, which are associated with multi-sums of products.
Integrability of reductions of the discrete KdV and potential KdV equations
A. N. W. Hone, P. H. van der Kamp, G. R. W. Quispel +1
We study the integrability of mappings obtained as reductions of the discrete Korteweg-de Vries (KdV) equation and of two copies of the discrete potential Korteweg-de Vries equatio…
Involutivity of integrals for sine-Gordon, modified KdV and potential KdV maps
Dinh T. Tran, P. H. van der Kamp, G. R. W. Quispel
Closed form expressions in terms of multi-sums of products have been given in \cite{Tranclosedform, KRQ} of integrals of sine-Gordon, modified Korteweg-de Vries and potential Korte…