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Level: BSc, MSci, MSc
Title: Discrete rotations and continued fractions
Supervisor:

Prof. Franco Vivaldi
Research Area: Dynamical Systems and Statistical Physics
Description:

When space is discretised, one of the simplest dynamical systems – the planar rotation – becomes extremely complicated. A connection exists between arithmetical properties of the angle of rotation and probabilistic properties of the discretised motion. These are to be studied and could also be explored numerically, with the aim of formulating conjectures.
Further Reading:
  • F. Vivaldi, Periodicity and transport from round-off errors, Experim. Math. 3 (1994) 303–315.
Key Modules:

MTH6128 Number Theory (essential)

MTH4107 Introduction to Probability (desirable)

MTH6107 Chaos and Fractals (desirable)
Other Information:

This project requires the ability to write simple computer programs (in C, say).
Current Availability: Yes