Admission requirements
Introduction to Probability (1st year)
Introduction to Measure Theory (2nd year)
Description
In this course we will discuss the differences between deterministic
and random dynamical systems, and the new phenomena arrising when the dynamics
is subject to random noise. We plan to discuss the following topics
Chaos Game and Iterated Function Systems
Products of random matrices
Lyapunov exponents
Ergodic theory of skew products (cocycles, Abramov-Rokhlin formula)
Stochastic stability
Course objectives
Learn basic notions in egrodic theory
Hyperbolicity, chaotic behavior
Notion of Lyapunov exponents,
Skew products, understand the difference between quenched and annealed results
Phenomenon of stochastic stability
Timetable
In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.
Additionally, you can easily link MyTimetable to a calendar app on your phone, and schedule changes will be automatically updated in your calendar. You can also choose to receive email notifications about schedule changes. You can enable notifications in Settings after logging in.
Questions? Watch the video, read the instructions, or contact the ISSC helpdesk.
Note: Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.
Mode of instruction
Lectures by Terhesiu, Verbitskiy
Student presentations (at the end)
Assessment method
Homework assignments (40%)
Final presentation (60%)
Reading list
1) V. Araujo, Random Dynamical Systems, https://arxiv.org/pdf/math/0608162.pdf
2) K. Dajani, Introduction to Ergodic Theory,
https://webspace.science.uu.nl/~kraai101/LectureNotesMM-2.pdf
3) L. Barreira, Lyapunov Exponents. https://doi.org/10.1007/978- 3- 319- 71261- 1
Relevant research papers will be provided.
Registration
As a student, you are responsible for enrolling on time through MyStudyMap.
In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.
Extensive information about the operation of MyStudyMap can be found here.
There are two enrolment periods per year:
Enrolment for the fall opens in July
Enrolment for the spring opens in December
See this page for more information about deadlines and enrolling for courses and exams.
Note:
It is mandatory to enrol for all activities of a course that you are going to follow.
Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.
Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.
Contact
Dr. Dalia Terhesiu, d.e.terhesiu[at]math.leidenuniv.nl
Remarks
Software
Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.