Applications of entropy compression algorithms to dynamical systems and fluid mechanics

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04986
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Chubu University (2017); Hokkaido University (2015-2016)
• Principal Investigator: ARAI Zin 中部大学, 創発学術院, 教授 (80362432)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 力学系 / アルゴリズム / 数値解析 / 数理モデル

Outline of Final Research Achievements

Using recent information theoretic methods such as the succinct data structure, we have developed some algorithms for improving the computational capability of graph theoretical methods in dynamical systems and fluid mechanics. These algorithms enable us to use compressed and memory-efficient data structures for computing the structure of the invariant sets of dynamical systems so that we can handle more practical and higher dimensional problems.
We also studied the relation between the information theoretic invariants and topological invariants of the system. In particular, we have shown that, for some dynamical systems, there is an explicit relation between the information theoretic entropy of the data required for the graph representation of the system and the topological entropy of the system.

Free Research Field

数学