Summability of Transseries Solution of Non-integrable Hamiltonian System

被引：0

作者：

Yoshino, Masafumi ^{[1
]}

机构：

[1] Hiroshima Univ, Grad Sch Adv Sci & Engn, Hiroshima 7398526, Japan

来源：

JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS | 2024年 / 30卷 / 02期

关键词：

Nonintegrability; Hamiltonian system; Transseries; Superintegrability;

D O I：

10.1007/s10883-024-09692-2

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper studies the summability of the transseries solution of a nonintegrable Hamiltonian system. Since our system has a resonance and is not integrable a general transseries theory does not work well as far as the author knows. In order to construct a formal transseries solution and prove its summability our main idea is to use the superintegrability of a Hamiltonian system in a class of transseries. More precisely we first show the superintegrability of a Hamiltonian system in the category of transseries via the key Lemmas 1 and 4 which follow. By virtue of the superintegrability we show the existence of a formal transseries solution. Then its summability is proved via the superintegrability. We note that the argument based on the superintegrability is elementary.

引用

页码：1 / 27

页数：27

共 50 条

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