School of Mathematical Sciences Colloquium Series logo




Professor Michael Barnsley (ANU)

The Entropy of an
Overlapping Dynamical System



Date & Time: Friday, March 23, 2012, 15:10

Location: Napier G03           

Abstract: The term "overlapping" refers to a certain fairly simple type of piecewise continuous function from the unit interval to itself and also to a fairly simple type of iterated function system (IFS) on the unit interval. A correspondence between these two classes of objects is used to: 
1. find a necessary and sufficient condition for a fractal transformation from the attractor of one overlapping IFS to the attractor of another overlapping IFS to be a homeomorphism and
2. find a formula for the topological entropy of the dynamical system associated with an overlapping function.  
These results suggest a new method for analysing clocks, weather systems and prime numbers.

The Colloquium will be followed by a reception for our speaker in the Staff Tea Room.

Note that on Thursday Michael Barnsley will also give a


 Public lecture at the Royal Institution of Australia


Super Fractals

Date & Time: Thursday, March 22, 2012, 18:00 - 19:30

Location: Royal Institution of Australia, The Science Exchange, 55 Exchange Place, Adelaide

Free, but booking required at RiAus web-page           


Abstract: Van Gogh said an artist should ‘ignore the obvious and exaggerate the essential.’ Fractal homeomorphisms enable us to do just that! The beautiful world of fractal geometry can be found in nature, from the shape of a shoreline to the curl of a fern frond. Fractals can also be used to transform pictures from nature.  Mathematician Michael Barnsley will demonstrate the intriguing images that result.

Michael Barnsley's web-page