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Prospectus

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Random Dynamical Systems (BM)

Course
2020-2021

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