Singular Perturbation of Nonlinear Systems with Regular Singularity

Autor(es)

Marchetti, Domingos H. U. ; Conti, William R. P.

• Tipo de documento: Artigo Científico
• Fonte: DISCRETE DYNAMICS IN NATURE AND SOCIETY; v. 2018, p. 10-pg., 2018-01-01.

Resumo

We extend Balser-Kostov method of studying summability properties of a singularly perturbed inhomogeneous linear system with regular singularity at origin to nonlinear systems of the form epsilon zf' = F(epsilon, z, f) with F a C-nu-valued function, holomorphic in a polydisc (D-rho) over barx (D-rho) over barx (D) over bar (nu). We show that its unique formal solution in power series of epsilon, whose coefficients are holomorphic functions of z, is 1-summ able under a Siegel-type condition on the eigenvalues of F-f(0, 0, 0). The estimates employed resemble the ones used in KAM theorem. A simple lemma is applied to tame convolutions that appear in the power series expansion of nonlinear equations. Applications to spherical Bessel functions and probability theory are indicated. The proposed summability method has certain advantages as it may be applied as well to (singularly perturbed) nonlinear partial differential equations of evolution type. (AU)

• Processo FAPESP: 07/59739-4 - Estudo da dinamica dos zeros de lee-yang induzida pela transformacao de grupo de renormalizacao no modelo n-vetorial e gases reais.
• Beneficiário: William Remo Pedroso Conti
• Modalidade de apoio: Bolsas no Brasil - Doutorado