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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Singular Perturbation of Nonlinear Systems with Regular Singularity

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Autor(es):
Marchetti, Domingos H. U. [1] ; Conti, William R. P. [2]
Número total de Autores: 2
Afiliação do(s) autor(es):
[1] Univ Sao Paulo, Inst Fis, Rua Matao 1371, BR-05508090 Sao Paulo, SP - Brazil
[2] Univ Fed Sao Paulo, Dept Ciencias Mar, Rua Dr Carvalho Mendonca 144, BR-11070100 Santos, SP - Brazil
Número total de Afiliações: 2
Tipo de documento: Artigo Científico
Fonte: DISCRETE DYNAMICS IN NATURE AND SOCIETY; 2018.
Citações Web of Science: 0
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 dinâmica dos zeros de Lee-Yang induzida pela transformação de grupo de renormalização no modelo n-vetorial e gases reais
Beneficiário:William Remo Pedroso Conti
Linha de fomento: Bolsas no Brasil - Doutorado