Seminar has been cancelled due to sickness.
Nikita Sidorov, The University of Manchester
“The doubling map with asymmetrical holes”
Let
T
denote
the
doubling
map
on
the
interval
[0,1]
and
let
0
<
a
<
b
<
1.
Denote
by
J(a,b)
the
set
of
all
x
in
[0,
1]
such
that
the
T
-orbit
of
x
has
an
empty
intersection
with
the
interval
(a,
b).
In
my
talk
I
am
going
to
give
a
full
description
of
(a,b)
such
that
J(a,b)
is
of
positive
Hausdorff
dimension.
This
description
will
involve
balanced
words
and
Sturmian
sequences.
I
will
also
explain
how
this
family
of
open
dynamical
systems
provides
explicit
“routes
to
chaos”
previously
observed
numerically
in
conventional
dynamical
systems.
This
talk
is
based
on
a
recent
joint
paper
with
Paul
Glendinning.