If
G
G
is the group of an oriented knot
k
k
, then the set
Hom
(
K
,
Σ
)
\operatorname {Hom} (K, \Sigma )
of representations of the commutator subgroup
K
=
[
G
,
G
]
K = [G,G]
into any finite group
Σ
\Sigma
has the structure of a shift of finite type
Φ
Σ
\Phi _{\Sigma }
, a special type of dynamical system completely described by a finite directed graph. Invariants of
Φ
Σ
\Phi _{\Sigma }
, such as its topological entropy or the number of its periodic points of a given period, determine invariants of the knot. When
Σ
\Sigma
is abelian,
Φ
Σ
\Phi _{\Sigma }
gives information about the infinite cyclic cover and the various branched cyclic covers of
k
k
. Similar techniques are applied to oriented links.