The first mechanic who checked it said that his diagnostic program didn't show anything wrong. So of course the car worked for about a week afterwards before becoming reticent.
Yet the next day it started all right. I took it to a second mechanic, whose diagnostics told him that the 'cam sensor' was bad. I won't even bother with the details of what such a thing is or how it works, but I do remember another van I had where that same thing went bad. When replaced, that van worked for the rest of its useful life.
Of course my Aveo worked for about a week and decided not to start again. And of further course it started immediately for that second mechanic, whom I took it back to as he had most recently dealt with it.
He's going to let me know what else he might find later. In the meanwhile, my horse, my horse, my kingdom for a horse!