6 papers
On difference-differential Lax pairs and integrals of Painlevé equations in finite characteristic
Nalini Joshi, Tomas Lasic Latimer, Pieter Roffelsen
We collect rank two difference-differential Lax pairs for classical Painlevé equations in the literature and put each in matrix form with the coefficient matrix of the…
On integrals of non-autonomous dynamical systems in finite characteristic
Nalini Joshi, Pieter Roffelsen
We use a difference Lax form to construct simultaneous integrals of motion of the fourth Painlevé equation and the difference second Painlevé equation over fields with finite chara…
Arithmetic dynamics of a discrete Painlevé equation
Nalini Joshi, Pieter Roffelsen
We consider the orbits of a discrete Painlevé equation over finite fields and show that the number of points in such orbits satisfy the Hasse bound. The orbits turn out to lie on a…
On the crystal limit of the q-difference sixth Painlevé equation
Nalini Joshi, Pieter Roffelsen
We consider the Riemann-Hilbert correspondence associated with the -difference sixth Painlevé equation in the crystal limit, i.e. , and show two main results. Fi…
Segre surfaces and geometry of the Painlevé equations
Nalini Joshi, Marta Mazzocco, Pieter Roffelsen
In this paper, we consider a six parameter family of affine Segre surfaces embedded in . For generic values of the parameters, this family is associated to the -dif…
Exponentially-improved asymptotics for -difference equations: and
Nalini Joshi, Adri Olde Daalhuis
Usually when solving differential or difference equations via series solutions one encounters divergent series in which the coefficients grow like a factorial. Surprisingly, in the…