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Geometric approach to a singular boundary value problem with turning points
The singularly perturbed boundary value problem
$\epsilon \ddot x=f(x,t;\epsilon)\dot x$, $x(-1;\epsilon)=A$,
$x(0;\epsilon)=B$ is studied as an application of the geometric singular perturbation theory for turning points. The key ingredients are: the delay of stability
loss that characterizes all possible singular orbits of the boundary value problem,
and the exchange lemmas for problems with turning points as the geometric tool
to show the existence of solutions shadowing singular orbits.