 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-1/31e/solution

Let

ϕ_{t} (x)

denote the flow through

x

α (x) = ⋂_{T < 0} \overline{{ϕ_{t} (x) : t < T}}, ω (x) = ⋂_{T > 0} \overline{{ϕ_{t} (x) : t > T}} .

Equivalently, they contain the limits of

ϕ_{t_{j}} (x)

t_{j} \to - \infty

and

t_{j} \to + \infty

, respectively.

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