Jeroen S.W. Lamb教授(Kyoto University / Imperial College London)によるスーパーグローバルコース数学特別講義を下記の要領で行います。
- 科目名
- スーパーグローバルコース数学特別講義2
- 日 時
- 2017年4月10日(月)〜14日(金)
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4月10日(月) 13:00〜15:00
4月11日(火) 13:00〜15:00
4月12日(水) 10:00〜12:00
4月13日(木) 10:00〜12:00
4月14日(金) 13:00〜15:00 - 場 所
- 京都大学理学部3号館 127大会議室
- 題 目
- Special Lecture on Random Dynamical Systems
- 概 要
- Dynamical systems describe the time-evolution of variables that characterize the state of a system. In deterministic autonomous dynamical systems, the corresponding equations of motion are independent of time and constant, but in random dynamical systems the equations of motion explicitly depend on a stochastic process or random variable.
- The development of the field of deterministic dynamical systems – including “chaos” theory - has been one of the scientific revolutions of the twentieth century, originating with the pioneering insights of Poincaré, providing a geometric qualitative understanding of dynamical processes, aiding and complementing analytical and quantitative viewpoints.
- Motivated by increasing demands on modelling from scientists, during the last decade there has been an increasing interest in time-dependent and in particular random dynamical systems, often described by stochastic differential equations. Despite the obvious scientific importance of the field, with applications ranging from physics and engineering to bio-medical and social sciences, a geometric qualitative theory for random dynamical systems is still in its infancy.
- This short course consists of an introduction to random dynamical systems, from a predominantly geometric point of view. The aim is to introduce basic concepts in the context of simple examples. We will discuss some elementary results and highlight open questions.
- The course is aimed at graduate students in the exact sciences. Some elementary background in dynamical systems and probability theory will be useful, but is not a strict prerequisite.
- Outline:
- 1. Barnsley’s “chaos game” as a random dynamical system.
- 2. Random circle maps: Lyapunov exponents and synchronisation.
- 3. A dynamical systems perspective of stochastic ordinary differential equations.
- 4. Set-valued dynamical systems describing the aggregate behaviour of random dynamical systems with bounded noise.
- 5. A random dynamical systems perspective of critical transitions and their early warning signals.
- 言 語
- 英語
- 備 考
- 本講義は録画し、Web上で公開します。講義室前方はカメラに写る場合がありますので、予めご了承下さい。