I have a hard time understanding a simple argument for the following. Quite often I find in papers that limit cycles before and after period-doubling bifurcations lie on the Möbius strip in the state-space. But anything similar I can not find in the Wiggins nor Guckenheimer/Holmes.
But still, what does it even mean? How can I understand it, like that the center manifold (associated with the original limit cycle) forms the Möbius strip in geometrical interpretation?