Study of connection problem for non-integrable Hamiltonian systems

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400118
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Hiroshima University
• Principal Investigator: Yoshino Masafumi 広島大学, 理学研究科, 教授 (00145658)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: ボレル総和法 / ハミルトン系 / 非可積分性 / 接続問題 / モノドロミー / Fuchsian equation / 特異摂動 / モーメント総話法

Outline of Final Research Achievements

We study the structure of non-integrability of a Hamiltonian system and the global　properties of solutions by using a singular first integral.The difficulty is to give the meaning to the divergent formal first integral or to the divergence of the normalizing transformation. We prove the Borel summability with respect to a certain parameter in the equation for first order system of partial differential equations. As for the non-integrability we show the semi-global non-integrability of a Hamiltonian system which is not analyzed by differential Galois theory. Because the global property of the first integral in the argument is not well understood, the result has the possibility to improve.

Free Research Field

関数方程式および力学系