Modern Dynamical Systems (S. K. Lando, A. S. Skripchenko) Spring 2025

Books and articles  Modern Dynamical Systems

Dear students,

here is the list of some useful links and materials for our course. 

1.  https://fuglede.dk/maths/notes/class/inthypgeom.pdf

Cool lectures by Subhojoy Gupta that start with hyperbolic geometry and Fuchsian groups

2.  http://www.weizmann.ac.il/math/sarigo/sites/math.sarigo/files/uploads/ergodicnotes.pdf

Different plots on ergodic theory (lectures by O. Sarig) 

3.  https://arxiv.org/abs/math/9607214

An important paper by Roy Adler on symbolic dynamics  

4.  http://people.math.harvard.edu/~ctm/math275/base/rs/course.pdf

Interesting course by C. McMullen

5.  https://arxiv.org/abs/math/0210301

Nice survey by D. Kleinbock on homogenous dynamics and its applications to number theory

6. introduction to Teichmüller dynamics by V. Delecroix: 

https://www.labri.fr/perso/vdelecro/Salta2015-notes.pdf

7. J. -C. Yoccoz on Teichmüller dynamics

https://www.college-de-france.fr/media/jean-christophe-yoccoz/UPL15305_PisaLecturesJCY2007.pdf

8. Nice letters on hyperbolic dynamics by A. Kocsard

https://w3.impa.br/~alejandro/docs/hyperbolic-2024-05-16.pdf

Why do people care about Fuchsian groups (math overflow discussion):

https://mathoverflow.net/questions/260193/why-are-fuchsian-groups-interesting?_gl=1*nup4mg*_ga*OTUyNDAzNjkxLjE2NzUwNzI3Njk.*_ga_S812YQPLT2*MTY3NTY3NDU4My4zLjEuMTY3NTY3NDYwOS4wLjAuMA

Some cool books (feel free to ask if you can not find a file) 

1. Françoise Dal'bo, Geodesic and Horocyclic Trajectories

2. B. Farb, D. Margalit, A primer on a mapping class groups

3. Я. Г. Синай, Введение в эргодическую теорию 

4. J. Aaronson, An introduction to Infinite Ergodic Theory

5. B. Hasselblat, A. Katok, Introduction to the Modern Theory of Dynamical Systems