Analytic Properties of Generating Function and Its Formal Derivatives for Dynamical System
Project/Area Number |
61540283
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Research Category |
Grant-in-Aid for General Scientific Research (C)
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Allocation Type | Single-year Grants |
Research Field |
物理学一般
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Research Institution | Nihon University |
Principal Investigator |
KONNO KIMIAKI College of Science and Technology, Assistant Professor, 理工学部, 助教授 (50059606)
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Project Period (FY) |
1986 – 1987
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Project Status |
Completed (Fiscal Year 1988)
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Budget Amount *help |
¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1987: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 1986: ¥500,000 (Direct Cost: ¥500,000)
|
Keywords | DYNAMICAL SYSTEM / CHAOS, GENERATING FUNCTION / LYAPUNOV EXPONENT / FUNCTIONAL EQUATION / 母関数 / 軌道不安定性 / 関数方程式 / ソリトン / 複素力学系 / リヤプノフ指数 / フラクタル / 可積分系 |
Research Abstract |
Generating function and its formal derivatives for one dimensional discrete dynamical systems are introduced. By taking its expansion parameter as complex, analytic properties of these functions are investigated. Especially it is found that the Lyapunov exponent is given by the radius of convergence of the first derivative function. Functional equations of these functions are also discussed. By introducing another one dimensional map in addition to the original one, a model of the generating function is given. It is found that the function is expressed as the basin boundary. Extending one of the independent variables into complex, nonlinear interactions between solitons for the integrable equations, such as the Korteweg-de Vries equation, the Boussinesq equation, the Hirota-Ito equation and the Toda lattice, are investigated by observing behavior of poles of soliton solutions.
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Report
(2 results)
Research Products
(2 results)