School of
Mathematical
Sciences Colloquium Series |
|
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