<s>
In	O
mathematics	O
,	O
Fatou	O
components	O
are	O
components	O
of	O
the	O
Fatou	B-Language
set	I-Language
.	O
</s>
<s>
then	O
for	O
a	O
periodic	O
component	O
of	O
the	O
Fatou	B-Language
set	I-Language
,	O
exactly	O
one	O
of	O
the	O
following	O
holds	O
:	O
</s>
<s>
is	O
a	O
Siegel	B-Algorithm
disc	I-Algorithm
:	O
a	O
simply	O
connected	O
Fatou	O
component	O
on	O
which	O
f(z )	O
is	O
analytically	O
conjugate	O
to	O
a	O
Euclidean	O
rotation	O
of	O
the	O
unit	O
disc	O
onto	O
itself	O
by	O
an	O
irrational	O
rotation	O
angle	O
.	O
</s>
<s>
is	O
a	O
Herman	B-Algorithm
ring	I-Algorithm
:	O
a	O
double	O
connected	O
Fatou	O
component	O
(	O
an	O
annulus	O
)	O
on	O
which	O
f(z )	O
is	O
analytically	O
conjugate	O
to	O
a	O
Euclidean	O
rotation	O
of	O
a	O
round	O
annulus	O
,	O
again	O
by	O
an	O
irrational	O
rotation	O
angle	O
.	O
</s>
<s>
and	O
t	O
=	O
6151732	O
...	O
will	O
produce	O
a	O
Herman	B-Algorithm
ring	I-Algorithm
.	O
</s>
