Recent applications of the theory of Lie systems in Ermakov systems.
Reduction of differential equations
Let (F,D) be a differential field with the subfield of constants C (c ∈ C iff Dc=0). We consider linear differential equations (1) , where , and the solution y is in F or in some extension E of F (E ⊇ F). There always exists a (minimal, unique) extension E of F, where Ly=0 has a full system of linearly independent (over C) solutions; it is called the Picard-Vessiot extension of F E = PV(F,Ly=0). The Galois group G(E|F) of an extension field E ⊇ F consists of all differential automorphisms of...
Remodified Bessel functions via coincidences and near coincidences.
Reproductivity of some equations of analysis. II.
Resolvent kernel for the Kohn Laplacian on Heisenberg groups.
Riccati equations.
Riccati's differential equation in birth-death processes.
This note reviews the occurrence of Riccati's equation in three birth-death type processes, and outlines their solutions.
Rigorous results on the power expansions for the integrals of a hamiltonian system near an elliptic equilibrium point