RDS&ET2025

Potential individual projects' description, the idea is to familiarise with the paper and working with some problems either closed or open and produce a report for assessment (60% written, 40% oral):

1)  Iterated function systems of affine expanding and contracting maps of the unit interval and their properties.

This project works closely with Ale Jan Homburg's paper: https://staff.fnwi.uva.nl/a.j.homburg/Files/220709987.pdf, with possible extension of working with different examples and proving open problems mentioned in the paper.

2) Synchronization properties of random piecewise isometries

From the lecture by Vincent Goverse and the paper: https://arxiv.org/abs/1408.1140.

3) Random dynamical systems with bounded noise: a boundary map approach

Understands the boundary map first introduced in https://arxiv.org/pdf/2303.01895, explore the simple case for linear map: https://arxiv.org/pdf/2310.03437 . Possible further investigation includes topological bifurcations of attractors in the set-valued mapping context: https://www.ma.ic.ac.uk/~jswlamb/papers/setvaluedbifpreprint.pdf or analogous version for flows:  https://www.researchgate.net/publication/366016533_On_Minimal_Invariant_Sets_of_Certain_Set-Valued_Dynamical_Systems_-_A_Boundary_Map_Approach