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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2019

Paper 1

Let $\phi_t(x)$ denote the <flow map>[flow] through $x$. Its <alpha-limit set> and <omega-limit set> are
$$
\alpha(x)=\bigcap_{T<0}\overline{\{\phi_t(x):t<T\}},
\qquad
\omega(x)=\bigcap_{T>0}\overline{\{\phi_t(x):t>T\}}.
$$
Equivalently, they contain the limits of $\phi_{t_j}(x)$ along sequences $t_j\to-\infty$ and $t_j\to+\infty$, respectively.

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 1 / 31E / Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 1 / 31E / Solution

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Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 1 / 31E / Solution

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