0 many and of several different types -- 繁多的，多种多样的
1 a pipe or closed space in a machine that has several openings, allowing liquids and gases to enter and leave -- （机器上使液体或气体能够出入的）多支管，歧管
Thus, is supported on a set which contains many full unstable manifolds.
We study the growth of unstable manifolds of automorphisms of complex surfaces.
The stable and unstable manifolds of the saddletype motions may intersect transversely, yielding chaotic fluid particle motions.
The center manifolds are transverse intersections of center stable manifolds with center unstable manifolds.
Both theorems are proved by establishing a dichotomy for the conditional measures of along the intersection of suitable stable manifolds.
In the process we saw that there were examples of non-isometric graph manifolds of non-positive curvature whose universal covers have equivalent boundaries.
One often considers oriented bordisms, which are oriented manifolds with boundary.
The motivation of the previous theorem is the classical problem of denseness of smooth conservative diffeomorphisms of compact manifolds.
