Top Global Course Special Lectures by Prof. Jeroen S.W. Lamb (Kyoto University / Imperial College London) will take place as follows:
- Course Title
- Top Global Course Special Lectures 2
- Date & Time
- April 10 - 14, 2017
Monday, April 10 13:00-15:00
Tuesday, April 11, 13:00-15:00
Wednesday, April 12 10:00-12:00
Thursday, April 13 10:00-12:00
Friday, April 14, 13:00-15:00
- 127 Conference room, Faculty of Science Bldg. #3, Kyoto University
- Special Lecture on Random Dynamical Systems
- 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.
- 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.
- This series of lectures will be video-recorded and made available online.
Please note that anyone in the front rows of the room can be captured by a video camera.