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2018 Fiscal Year Final Research Report

Ergodic theory of number theoretic transformations toward the construction of infinite ergodic theory

Research Project

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Project/Area Number 15K17559
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionJapan Women's University

Principal Investigator

Natsui Rie  日本女子大学, 理学部, 准教授 (60398633)

Project Period (FY) 2015-04-01 – 2019-03-31
Keywordsエルゴード理論 / 測度論的数論 / 複素連分数変換 / ユークリッドアルゴリズム
Outline of Final Research Achievements

Toward the goal finding a new invariant which is captured the difference in the notion between determinism and randomness on measurable dynamical systems with infinite invariant measure, this research is focused on the randomness of number generated from number theoretic transformations. In particular, this research obtained the result about the properties of complexity for nearest integer complex continued fraction transformations over imaginary quadratic field and number theoretic algorithms over non-Archimedean field.

Free Research Field

エルゴード理論

Academic Significance and Societal Importance of the Research Achievements

未だに一般的体系が構築されていない無限大不変測度を持つ可測力学系に対するエルゴード理論において、determinismとrandomnessの概念の違いを捉える新たな不変量を見つけるために具体的な数論的変換から生まれる数の持つランダム性に着目し、その複雑性に関する研究成果を得た。数論的変換から生まれる数の複雑性に関する本研究成果は理論計算機科学と密接に結びついており、現代において必要不可欠である計算機の高速性や精度の向上に繋がることを期待する。

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Published: 2020-03-30  

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