Tom Tucker, Rochester University
“Integral points in two-parameter orbits”
Let
K
be
a
number
field,
let
f
:
P1
−
−
>
P1
be
a
nonconstant
rational
map
of
degree
greater
than
1
that
is
not
conjugate
to
a
powering
map,
let
S
be
a
finite
set
of
places
of
K,
and
suppose
that
u,winP1(K)
are
not
preperiodic
under
f.
We
prove
that
the
set
of
(m,n)inN2
such
that
fm(u)
is
S-integral
relative
to
fn(w)
is
finite
and
effectively
computable.
This
may
be
thought
of
as
a
two-parameter
analog
of
a
result
of
Silverman
on
integral
points
in
orbits
of
rational
maps.
Please note the special date.