Rodica D. Costin Research Statement
نویسنده
چکیده
My research is focused on differential equations, with emphasis on the study of singularities and asymptotic behavior of solutions, regularity, normal forms, the study of non-integrable systems and connection to chaos. I am applying new methods—analysis of equations in Borel space (after inverse Laplace transform) and a theory of generalized Borel summation of general formal solutions (transseries).
منابع مشابه
Rigorous Bounds of Stokes Constants for Some Nonlinear Odes at Rank One Irregular Singularities
A rigorous way to obtain sharp bounds for Stokes constants is introduced and illustrated on a concrete problem arising in applications.
متن کاملFailure of Analytic Hypoellipticity in a Class of Differential Operators
For the hypoelliptic differential operators P = ∂ x + ( x∂y − x∂t 2 introduced by T. Hoshiro, generalizing a class of M. Christ, in the cases of k and l left open in the analysis, the operators P also fail to be analytic hypoelliptic (except for (k, l) = (0, 1)), in accordance with Treves’ conjecture. The proof is constructive, suitable for generalization, and relies on evaluating a family of e...
متن کاملThe First Return Map for Planar Vector Fields with Nilpotent Linear Part with a Center or a Focus
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 whose terms can be calculated iteratively. The first nontrivial coefficient is the value of an Abelian integral, and the following ones are explicitly given as iterated integrals built with algebraic functions.
متن کاملThe Return Map for a Planar Vector Field with Nilpotent Linear Part: A Direct and Explicit Derivation
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 identity and whose terms can be calculated iteratively. The first nontrivial coefficient is the value of an Abelian integral, and the following ones are explicitly given as iterated integrals.
متن کاملNonlinear Perturbations of Fuchsian Systems: Corrections and Linearization, Normal Forms
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 linear part (they are not linearizable) and the obstructions are found constructively, as a countable set of numbers. Furthermore, assuming a polynomial character of the nonlinear part, it is shown that there exists a u...
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