Let f be a continuous map of a closed interval I into itself. A point
x
∈
I
x \in I
is called a homoclinic point of f if there is a peridoic point p of f such that
x
≠
p
,
x
x \ne p,x
is in the unstable manifold of p, and p is in the orbit of x under
f
n
{f^n}
, where n is the period of p. It is shown that f has a homoclinic point if and only if f has a periodic point whose period is not a power of 2. Furthermore, in this case, there is a subset X of I and a positive integer n, such that
f
n
(
X
)
=
X
{f^n}(X) = X
and there is a topological semiconjugacy of
f
n
:
X
→
X
{f^n}:X \to X
onto the full (one-sided) shift on two symbols.