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
Mode of instruction
Lectures by Terhesiu, Verbitskiy
Student presentations (at the end)
Assessment method
Homework assignments (40%)
Final presentation (60%)
Literature
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.
Contact
Dr. Dalia Terhesiu, d.e.terhesiu[at]math.leidenuniv.nl
Dr. Evgeny Verbitskiy, evgeny[at]math.leidenuniv.nl