For a complementary perspective, we can fix a point \\(x \in M\\), and let \\(t\\) vary, to get the trajectory function \\(\phi_x(t) = \phi^t(x)\\).

The _orbit_ of \\(x\\) is the image of its trajectory function \\(\phi_x\\).

The _orbit_ of \\(x\\) is the image of its trajectory function \\(\phi_x\\).