Let
X
X
be a compact Kähler manifold of dimension
3
3
and let
f
:
X
→
X
f:X\rightarrow X
be a pseudo-automorphism. Under the mild condition that
λ
1
(
f
)
2
>
λ
2
(
f
)
\lambda _1(f)^2>\lambda _2(f)
, we prove the existence of invariant positive closed
(
1
,
1
)
(1,1)
and
(
2
,
2
)
(2,2)
currents, and we also discuss the (still open) problem of intersection of such currents. We prove a weak equi-distribution result for Green
(
1
,
1
)
(1,1)
currents of meromorphic selfmaps, not necessarily algebraic
1
1
-stable, of a compact Kähler manifold of arbitrary dimension and discuss how a stronger equidistribution result may be proved for pseudo-automorphisms in dimension
3
3
. As a byproduct, we show that the intersection of some dynamically related currents is well-defined with respect to our definition here, even though not obviously to be seen so using the usual criteria.