09/29/2008, 01:03 AM
As I now see, even if the uniqueness criterion is valid, the precondition:
for each )
can not be true for any
for
(and probably for each
)!
Michał Misiurewicz [1] showed 1981 that the Julia set of
is the whole
(that is not directly visible from the
fractal). The Julia set is the boundary of the set
of all
such that
. That means that the set
and its complement
is dense in
. In every neighborhood of any complex number
there is a complex number
such that
and also a
such that
!
And that implies that
, which contains an open non-empty set, always contains points
such that
.
[1] Michał Misiurewicz (1981). On iterates of e^z. Ergodic Theory and Dynamical Systems, 1 , pp 103-106, doi:10.1017/S014338570000119X
can not be true for any
Michał Misiurewicz [1] showed 1981 that the Julia set of
And that implies that
[1] Michał Misiurewicz (1981). On iterates of e^z. Ergodic Theory and Dynamical Systems, 1 , pp 103-106, doi:10.1017/S014338570000119X