40 citations · 79 across the 6 of their papers we have counts for
6 papers
Optimal uniform estimates and rigorous asymptotics beyond all orders for a class of ODE's
O. Costin, M. D. Kruskal
For first order differential equations of the form and second order homogeneous linear differential equations with locally integrab…
On optimal truncation of divergent series solutions of nonlinear differential systems; Berry smoothing
O. Costin, M. D. Kruskal
We prove that for divergent series solutions of nonlinear (or linear) differential systems near a generic irregular singularity, the common prescription of summation to the least t…
Movable singularities of solutions of difference equations in relation to solvability and a study of a superstable fixed point
O. Costin, M. D. Kruskal
A unique analytic continuation result is proven for solutions of a relatively general class of difference equations by using techniques of generalized Borel summability. We overvie…
Borel summation of adiabatic invariants
O. Costin, L. Dupaigne, M. D. Kruskal
Borel summation techniques are developed to obtain exact invariants from formal adiabatic invariants (given as divergent series in a small parameter) for a class of differential eq…
Analytic methods for obstruction to integrability in discrete dynamical systems
O. Costin, M. D. Kruskal
A unique analytic continuation result is proved for solutions of a relatively general class of difference equations, using techniques of generalized Borel summability. This continu…
Analytic and Asymptotic Methods for Nonlinear Singularity Analysis: a Review and Extensions of Tests for the Painlevé Property
Martin D. Kruskal, Nalini Joshi, Rod Halburd
The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In parti…