
Theory on meromorphic
functions, used to describe many physical phenomena and engineering
problems, is being advanced by research at The University of Hong
Kong.
A
better understanding of factorisation and the complex dynamics of
the functions will help mathematicians and physicists alike, says
Dr Tuenwai Ng.
Factorisation
is about how a meromorphic function can become a function within
a function. Complex dynamics studies how a function behaves under
repeated substitutions.
The
behaviors can be represented graphically by Julia Sets (pictured
right). One distinctive property of the Julia Set is its selfsimilarity;
individual cells have the same pattern as larger blocks of cells.
“The dynamical process is as chaotic as can be,” said
Dr Ng.
Many
physics and engineering problems involve discovering the location
of zeros, or critical points, of a function.
Often,
zerofinding algorithms involve repeated substitutions and therefore
a good knowledge of complex dynamics is important to understanding
their efficiencies, said Dr Ng.
Principal
Investigator
Dr Tuenwai Ng : ntw@maths.hku.hk
