Asymptotic expansion of the period function II

被引：4

作者：

Saavedra, M ^{[1
]}

机构：

[1] Univ Concepcion, Fac Ciencias Fis & Matemat, Dept Matemat, Concepcion, Chile

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2006年 / 222卷 / 02期

关键词：

vector field; polycycle; desingularization; period function; asymptotic expansion;

D O I：

10.1016/j.jde.2005.04.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let P be a not necessarily bounded polycycle of an analytic vector field on an open set of the plane. Suppose that the singularities which appear after desingularization of the vertices of P are hyperbolic. Consider the function T defined by the return time near P. It is shown that the function T and its derivative T' have asymptotic expansions similar to the series of Dulac but with negative powers. (c) 2005 Published by Elsevier Inc.

引用

页码：476 / 486

页数：11

共 50 条

[1] Asymptotic expansion of the period function
Saavedra, M
JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 193 (02) : 359 - 373
[2] ASYMPTOTIC-EXPANSION OF PERIOD FUNCTION
SAAVEDRA, M
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1994, 319 (06): : 563 - 566
[3] ON THE ASYMPTOTIC EXPANSION OF THE LOGARITHM OF BARNES TRIPLE GAMMA FUNCTION II
Koumandos, Stamatis
Pedersen, Henrik L.
MATHEMATICA SCANDINAVICA, 2017, 120 (02) : 291 - 304
[4] The asymptotic expansion of the generalized Bessel function
Wright, EM
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1935, 38 : 257 - 270
[5] An asymptotic expansion related to the Dickman function
K. Soundararajan
The Ramanujan Journal, 2012, 29 : 25 - 30
[6] New asymptotic expansion for the Gamma function
Gergő Nemes
Archiv der Mathematik, 2010, 95 : 161 - 169
[7] Asymptotic expansion for the magnetoconductance autocorrelation function
Pluhar, Z
Weidenmüller, HA
ANNALS OF PHYSICS, 1999, 272 (02) : 295 - 319
[8] On the asymptotic expansion of Whittaker's function
Pevnyi, BG
COMPTES RENDUS DE L ACADEMIE DES SCIENCES DE L URSS, 1940, 28 : 308 - 309
[9] An asymptotic expansion related to the Dickman function
Soundararajan, K.
RAMANUJAN JOURNAL, 2012, 29 (1-3): : 25 - 30
[10] On the asymptotic expansion of the airy function.
Segala, F
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 1999, 2B (03): : 707 - 714

← 1 2 3 4 5 →