On the creation of chaos in higher dimensions
About this project
- Japan Grant Number
- JP18H01138
- Funding Program
- Grants-in-Aid for Scientific Research
- Funding organization
- Japan Society for the Promotion of Science
- Project/Area Number
- 18H01138
- Research Category
- Grant-in-Aid for Scientific Research (B)
- Allocation Type
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- Single-year Grants
- Review Section / Research Field
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- Basic Section 12040:Applied mathematics and statistics-related
- Research Institution
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- Tokyo Institute of Technology
- Chubu University
- Project Period (FY)
- 2018-04-01 〜 2023-03-31
- Project Status
- Completed
- Budget Amount*help
- 17,030,000 Yen (Direct Cost: 13,100,000 Yen Indirect Cost: 3,930,000 Yen)
Research Abstract
This study aims to elucidate the mechanisms by which chaotic behavior arises in high-dimensional dynamical systems, thereby contributing to the application of chaos theory. Specifically, we focused on the structure of the parameter space of the Henon map. We found inherently new structures of the set corresponding to connected Julia sets, which can not be achieved by perturbation from one-dimensional theory. This result refines our understanding of the structure of the parameter space of the Henon map, which is a fundamental problem in the study of high-dimensional chaotic dynamical systems. To achieve this goal, we developed several algorithms for computer-assisted proofs, including numerical methods to explore the structure of parameter space efficiently, validated numerical computations of the unstable manifolds of fixed points, and algorithms to evaluate the Green's function and mathematically rigorously prove the existence of its singularities.
Details 詳細情報について
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- CRID
- 1040282256969204992
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- Text Lang
- ja
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- Data Source
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- KAKEN
