School of Mathematics and Statistics

Postgraduate research

Research being undertaken by our current postgraduates:

Contact

Paul Wright


Supervisors

Start date

Aug 2010

Submission date

Paul Wright

Thesis

Dimensional Characteristics of the Non-Wandering Set of Open Billiards

Summary

This project will attempt to investigate the effects of moving and deforming obstacles in a dynamical billiard. Of particular interest is the effect on the Hausdorff dimension of the non-wandering set of the billiard ball map. Estimates of the Hausdorff dimension exist that depend on the position of obstacles, and estimates have been calculated for some cases using simulations and physical models [22], but there is no known method of calculating it exactly. An exact value may never be found for any billiard, but I will attempt to determine if the Hausdorff dimension depends continuously or smoothly on the position of obstacles, find as estimate for the derivative of the dimension with respect to some parameters, and investigate other properties of the non-wandering set, such as topological entropy, Lyapunov estimate and other kinds of dimension.

Why my research is important

The dependence of Hausdorff dimension on parameters of a set is an interesting open problem for many fractals and dynamical systems. Some of the techniques developed to solve this problem may be applied to similar dimension theory problems in a wide range of dynamical systems. The project will also extend our understanding of open billiard systems, which are used in some areas of mathematical physics.



Statistics clinic

Assistance in statistics is available for Postgraduates students by research at the UWA Centre for Applied Statistics.

 

School of Mathematics and Statistics

This Page

Last updated:
Monday, 16 June, 2014 2:41 PM

http://www.maths.uwa.edu.au/275877