<s>
In	O
mathematics	O
,	O
a	O
Bratteli	O
–	O
Veršik	O
diagram	O
is	O
an	O
ordered	O
,	O
essentially	O
simple	O
Bratteli	B-Algorithm
diagram	I-Algorithm
(	O
V	O
,	O
E	O
)	O
with	O
a	O
homeomorphism	O
on	O
the	O
set	O
of	O
all	O
infinite	O
paths	O
called	O
the	O
Veršhik	O
transformation	O
.	O
</s>
<s>
Let	O
X	O
={(	O
e1	O
,	O
e2	O
,...	O
)	O
|	O
ei∈Ei	O
and	O
r(ei )	O
=s	O
( ei+1	O
)	O
}	O
be	O
the	O
set	O
of	O
all	O
paths	O
in	O
the	O
essentially	O
simple	O
Bratteli	B-Algorithm
diagram	I-Algorithm
(	O
V	O
,	O
E	O
)	O
.	O
</s>
<s>
The	O
Veršhik	O
transformation	O
allows	O
us	O
to	O
construct	O
a	O
pointed	O
topological	O
system	O
(	O
X	O
,	O
φ	O
,	O
y	O
)	O
out	O
of	O
any	O
given	O
ordered	O
,	O
essentially	O
simple	O
Bratteli	B-Algorithm
diagram	I-Algorithm
.	O
</s>
<s>
This	O
is	O
the	O
notion	O
of	O
equivalence	O
used	O
for	O
Bratteli	B-Algorithm
diagrams	I-Algorithm
.	O
</s>
<s>
The	O
major	O
result	O
in	O
this	O
field	O
is	O
that	O
equivalent	O
essentially	O
simple	O
ordered	O
Bratteli	B-Algorithm
diagrams	I-Algorithm
correspond	O
to	O
topologically	O
conjugate	O
pointed	O
dynamical	O
systems	O
.	O
</s>
