85 citations · 158 across the 28 of their papers we have counts for
22 papers · 1 filter
Long time evolution of the Hénon-Heiles system for small energy
Ovidiu Costin, Rodica Costin, Kriti Sehgal
The Hénon-Heiles system, initially introduced as a simplified model of galactic dynamics, has become a paradigmatic example in the study of nonlinear systems. Despite its simplicit…
Parabolic cylinder functions revisited using the Laplace transform
Rodica D. Costin, Georgios Mavrogiannis
In this paper we gather and extend classical results for parabolic cylinder functions, namely solutions of the Weber differential equations, using a systematic approach by Borel-La…
On the domain of convergence of spherical harmonic expansions
O. Costin, R. D. Costin, C. Ogle +1
Spherical harmonic expansions (SHEs) play an important role in most of the physical sciences, especially in physical geodesy. Despite many decades of investigation, the large order…
Truncated Solutions of Painlevé Equation
Rodica D. Costin
We obtain convergent representations (as Borel summed transseries) for the five one-parameter families of truncated solutions of the fifth Painlevé equation with nonzero parameters…
A new type of factorial series expansions and applications
O. Costin, R. D. Costin
We construct a new type of convergent asymptotic representations, dyadic factorial expansions. Their convergence is geometric and the region of convergence can include Stokes rays,…
Jacobi series for general parameters and applications
Rodica D. Costin, Marina David
Representation of analytic functions as convergent series in Jacobi polynomials is reformulated using a unified approach for almost all complex . The coefficien…
Tronquée solutions of the Painlevé equation \P1
O. Costin, R. D. Costin, M. Huang
We analyze the one parameter family of tronquée solutions of the Painlevé equation \P1 in the pole-free sectors together with the region of the first array of poles. We find a conv…
A direct method to find Stokes multipliers in closed form for P1 and more general integrable systems
Ovidiu Costin, Rodica Costin, Min Huang
We introduce a new rigorous method, based on Borel summability and asymptotic constants of motion generalizing \cite{invent} and \cite{ode1}, to analyze singular behavior of nonlin…
The first return map for planar vector fields with nilpotent linear part with a center or a focus
Rodica D. Costin
The return map for planar vector fields with nilpotent linear part (having a center or a focus and under an assumption generically satisfied) is found as a convergent power series…
The return map for a planar vector field with nilpotent linear part: a direct and explicit derivation
Rodica D. Costin
Using a direct approach the return map near a focus of a planar vector field with nilpotent linear part is found as a convergent power series which is a perturbation of the identit…
Orthogonality of Jacobi and Laguerre polynomials for general parameters via the Hadamard finite part
Rodica D. Costin
Orthogonality of the Jacobi and of Laguerre polynomials, P_n^(a,b) and L_n^(a), is established for a,b complex (a,b not negative integers and a+b different from -2,-3,...) using th…
Differential systems with Fuchsian linear part: correction and linearization, normal forms and multiple orthogonal polynomials
Rodica D. Costin
Differential systems with a Fuchsian linear part are studied in regions including all the singularities in the complex plane of these equations. Such systems are not necessarily an…
Matrix valued polynomials generated by the scalar-type Rodrigues' formulas
Rodica D. Costin
The properties of matrix valued polynomials generated by the scalar-type Rodrigues' formulas are analyzed. A general representation of these polynomials is found in terms of produc…
A class of matrix-valued polynomials generalizing Jacobi Polynomials
Rodica D. Costin
A hierarchy of matrix-valued polynomials which generalize the Jacobi polynomials is found. Defined by a Rodrigues formula, they are also products of a sequence of differential oper…
Analytic linearization of nonlinear perturbations of Fuchsian systems
Rodica D. Costin
Nonlinear perturbation of Fuchsian systems are studied in regions including two singularities. Such systems are not necessarily analytically equivalent to their linear part (they a…
Nonlinear perturbations of Fuchsian systems: corrections and linearization, normal forms
Rodica D. Costin
Nonlinear perturbation of Fuchsian systems are studied in a region including two singularities. It is proved that such systems are generally not analytically equivalent to their li…
Rigorous WKB for finite order linear recurrence relations with smooth coefficients
O. Costin, R. D. Costin
We study the behavior of recurrence relations of the type $k\in \zdd$ ( fixed). The are functions in each variable…
Rigorous bounds of Stokes constants for some nonlinear ODEs at rank one irregular singularities
O. Costin, R. D. Costin, M. Kohut
A rigorous way to obtain sharp bounds for Stokes constants is introduced and illustrated on a concrete problem arising in applications.
Failure of analytic hypoellipticity in a class of PDOs
O Costin, R D Costin
For the hypoelliptic differential operators introduced by T. Hoshiro, generalizing a class of M. Christ, in the cases of …
Asymptotic properties of a family of solutions of the Painleve equation PVI
O Costin, R D Costin
In this paper we study the asymptotic behavior for large argument of a family of solutions of the Painlevé equation P$_{\rm VI} arising in the context of Random Matrix Theory [1].…
On the formation of singularities of solutions of nonlinear differential systems in antistokes directions
O. Costin, R. D. Costin
We determine the position and the type of spontaneous singularities of solutions of generic analytic nonlinear differential systems in the complex plane, arising along antistokes d…
Singular normal form for the Painlevé equation P1
Ovidiu Costin, Rodica Daniela Costin
We show that there exists a rational change of coordinates of Painlevé's P1 equation and of the elliptic equation after which these two equations become ana…