学部・大学院区分
Undergraduate / Graduate		理学部
時間割コード
Registration Code		0617500
科目区分
Course Category		専門科目
Specialized Courses
科目名　【日本語】
Course Title		解析学Ⅲ
科目名　【英語】
Course Title		Analysis Ⅲ
コースナンバリングコード
Course Numbering Code
担当教員　【日本語】
Instructor		JAERISCH Johannes Klaus B ○
担当教員　【英語】
Instructor		JAERISCH Johannes Klaus Bernhard ○
単位数
Credits		2
開講期・開講時間帯
Term / Day / Period		春 火曜日 ３時限
Spring Tue 3
授業形態
Course style		講義
Lecture
学科・専攻
Department / Program
数理学科
必修・選択
Compulsory / Selected
選択


授業の目的　【日本語】
Goals of the Course(JPN)
Fractal geometry and dynamical systems

The purpose of this course is twofold. Firstly, we aim to introduce mathematical concepts and ideas to deal with highly irregular fractal sets. Secondly, for fractal sets arising in the framework of dynamical systems, we study the interplay of fractal geometry and dynamical systems.
授業の目的　【英語】
Goals of the Course
到達目標　【日本語】
Objectives of the Course(JPN))
To get an idea of irregularity and self-similarity of fractal sets. To study the mathematical framework to define fractals sets, and to develop the mathematical tools to study properties of fractals sets, such as dimension and measure. Moreover, to study the interplay of fractal geometry and dynamical systems.
到達目標　【英語】
Objectives of the Course
授業の内容や構成
Course Content / Plan
Preliminaries from Measure theory and Topology.
Hausdorff dimension (Definition, Examples, Properties)
Mass distribution principles
Potential-theoretic methods and projection theorems
Iterated function systems (Banach fixed point theorem, Attractors, Bowen's formula for the Hausdorff dimension)
Limit sets of Schottky groups
履修条件
Course Prerequisites
Basics from analysis, real analysis (measure theory), and point-set topology.
関連する科目
Related Courses
Lectures on analysis, (point set) topology and measure theory.
This course is extends 解析学概論 Ⅳ(Introduction to AnalysisⅣ). Although there is some overlap, the two courses are basically independent.
成績評価の方法と基準
Course Evaluation Method and Criteria
Grading based on reports and quizzes.
不可(F)と欠席(W)の基準
Criteria for "Fail (F)" & "Absent (W)" grades
参考書
Reference Book
M. Barnsley. Fractals everywhere. Academic Press, 1988.
F. Dal’Bo. Geodesic and horocyclic trajectories: Universitext. Springer-Verlag London, Ltd.,London; EDP Sciences, Les Ulis, 2011.
K. Falconer. Mathematical foundations and applications. Third edition. John Wiley and Sons,Ltd., Chichester, 2014
Y. Pesin, V. Climenhaga. Lectures on Fractal Geometry and Dynamical Systems, AMS 2009.
教科書・テキスト
Textbook
Recommended books will be introduced on an individual basis.
課外学習等（授業時間外学習の指示）
Study Load(Self-directed Learning Outside Course Hours)
注意事項
Notice for Students
The lectures are in English.
他学科聴講の可否
Propriety of Other department student's attendance
可
他学科聴講の条件
Conditions for Other department student's attendance
Please contact me for details.
レベル
Level
2
キーワード
Keyword
Fractals, irregular sets, self-similar set, fractal dimension, topological entropy, topological pressure, iterated function system, Schottky groups
履修の際のアドバイス
Advice
To review the lectures carefully.
授業開講形態等
Lecture format, etc.
遠隔授業（オンデマンド型）で行う場合の追加措置
Additional measures for remote class (on-demand class)