The construction of the infinite ergodic theory and the application to metric number theory

2014 Fiscal Year Final Research Report

• Project/Area Number: 23740088
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Japan Women's University
• Principal Investigator: NATSUI Rie 日本女子大学, 理学部, 准教授 (60398633)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: エルゴード理論 / 測度論的数論 / ユークリッドアルゴリズム / 連分数変換

Outline of Final Research Achievements

Toward a construction of a general system for the measurable dynamical system with the infinite invariant measure, this research tried to find the new interpretation about the randomness of number from the point of view of the ergodic theory. In particular, this research obtained some results for the complexity of number about number theoretic transformations, for example Euclidean algorithm in the positive characteristic theory, Farey maps on the Bruhat-Tits tree, and α-continued fraction transformations on a real number field, as the concrete research model.

Free Research Field

エルゴード理論