<s>
The	O
standard	B-Algorithm
map	I-Algorithm
(	O
also	O
known	O
as	O
the	O
Chirikov	O
–	O
Taylor	O
map	O
or	O
as	O
the	O
Chirikov	B-Algorithm
standard	I-Algorithm
map	I-Algorithm
)	O
is	O
an	O
area-preserving	O
chaotic	O
map	O
from	O
a	O
square	O
with	O
side	O
onto	O
itself	O
.	O
</s>
<s>
It	O
is	O
constructed	O
by	O
a	O
Poincaré	O
's	O
surface	O
of	O
section	O
of	O
the	B-Algorithm
kicked	I-Algorithm
rotator	I-Algorithm
,	O
and	O
is	O
defined	O
by	O
:	O
</s>
<s>
The	O
properties	O
of	O
chaos	O
of	O
the	O
standard	B-Algorithm
map	I-Algorithm
were	O
established	O
by	O
Boris	O
Chirikov	O
in	O
1969	O
.	O
</s>
<s>
This	O
map	O
describes	O
the	O
Poincaré	O
's	O
surface	O
of	O
section	O
of	O
the	O
motion	O
of	O
a	O
simple	O
mechanical	O
system	O
known	O
as	O
the	B-Algorithm
kicked	I-Algorithm
rotator	I-Algorithm
.	O
</s>
<s>
The	B-Algorithm
kicked	I-Algorithm
rotator	I-Algorithm
consists	O
of	O
a	O
stick	O
that	O
is	O
free	O
of	O
the	O
gravitational	O
force	O
,	O
which	O
can	O
rotate	O
frictionlessly	O
in	O
a	O
plane	O
around	O
an	O
axis	O
located	O
in	O
one	O
of	O
its	O
tips	O
,	O
and	O
which	O
is	O
periodically	O
kicked	O
on	O
the	O
other	O
tip	O
.	O
</s>
<s>
The	O
standard	B-Algorithm
map	I-Algorithm
is	O
a	O
surface	O
of	O
section	O
applied	O
by	O
a	O
stroboscopic	O
projection	O
on	O
the	O
variables	O
of	O
the	B-Algorithm
kicked	I-Algorithm
rotator	I-Algorithm
.	O
</s>
<s>
The	O
constant	O
K	O
measures	O
the	O
intensity	O
of	O
the	O
kicks	O
on	O
the	B-Algorithm
kicked	I-Algorithm
rotator	I-Algorithm
.	O
</s>
<s>
The	B-Algorithm
kicked	I-Algorithm
rotator	I-Algorithm
approximates	O
systems	O
studied	O
in	O
the	O
fields	O
of	O
mechanics	O
of	O
particles	O
,	O
accelerator	O
physics	O
,	O
plasma	O
physics	O
,	O
and	O
solid	O
state	O
physics	O
.	O
</s>
<s>
Thus	O
,	O
the	O
structure	O
of	O
the	O
beam	O
can	O
be	O
approximated	O
by	O
the	O
kicked	B-Algorithm
rotor	I-Algorithm
.	O
</s>
<s>
For	O
the	O
map	O
is	O
linear	O
and	O
only	O
periodic	O
and	O
quasiperiodic	O
orbits	B-Algorithm
are	O
possible	O
.	O
</s>
<s>
When	O
plotted	O
in	O
phase	O
space	O
(	O
the	O
θp	O
plane	O
)	O
,	O
periodic	O
orbits	B-Algorithm
appear	O
as	O
closed	O
curves	O
,	O
and	O
quasiperiodic	O
orbits	B-Algorithm
as	O
necklaces	O
of	O
closed	O
curves	O
whose	O
centers	O
lie	O
in	O
another	O
larger	O
closed	O
curve	O
.	O
</s>
<s>
This	O
is	O
illustrated	O
in	O
the	O
figure	O
,	O
which	O
displays	O
a	O
collection	O
of	O
different	O
orbits	B-Algorithm
allowed	O
to	O
the	O
standard	B-Algorithm
map	I-Algorithm
for	O
various	O
values	O
of	O
.	O
</s>
<s>
All	O
the	O
orbits	B-Algorithm
shown	O
are	O
periodic	O
or	O
quasiperiodic	O
,	O
with	O
the	O
exception	O
of	O
the	O
green	O
one	O
that	O
is	O
chaotic	O
and	O
develops	O
in	O
a	O
large	O
region	O
of	O
phase	O
space	O
as	O
an	O
apparently	O
random	O
set	O
of	O
points	O
.	O
</s>
<s>
The	O
standard	B-Algorithm
map	I-Algorithm
is	O
related	O
to	O
the	O
circle	O
map	O
,	O
which	O
has	O
a	O
single	O
,	O
similar	O
iterated	O
equation	O
:	O
</s>
<s>
for	O
the	O
standard	B-Algorithm
map	I-Algorithm
,	O
the	O
equations	O
reordered	O
to	O
emphasize	O
similarity	O
.	O
</s>
