A first course in the beautiful, twisted shapes
known as fractals, and the way they are connected with
dynamical systems.
a one-semester course
at the National University
of Ireland, Maynooth. The material was intended to be covered
in three lectures and one tutorial per week.
The class is typically quite mixed, and the book aims
to challenge students familiar with rigorous arguments
while simultaneously providing comfort to other students
that prefer procedural mathematics---not an easy balancing act!
For instance, some exercises are targeted at one or other of these
two groups of students and, while some material is done in the context
of metric spaces, guidance is given to the reader who prefers to stick
to the real line.
This second edition of the book has no major new topics, but it is
about twice as long as the first. Some topics are explored in greater
depth (e.g. conjugacy and semiconjugacy, bifurcation) and some proofs
have been added (notably for Sharkovsky's and Singer's theorems).
Additional exercises have been given, and the most
challenging ones are marked with one or two stars.
The Irish-language first edition is
Codaigh agus Corais Dhinimiciula Readacha,
ISBN 0954426959.
A second edition will appear in due course.
BSc and MSc degrees in Mathematics from
University College, Cork, and won the National
University Travelling Studentship. He took the
PhD at the University of Chicago, under the supervision of
Robert Fefferman, and then worked at the University
of Michigan at Ann Arbor before returning to
Ireland to work at Maynooth. He is now Professor
of Mathematics and Head of Department at Maynooth.
He is a member of the Royal Irish Academy.
