Dynamical asymmetry is $C^1$-typical

here is an unrelated string of tex: A {\em bifoliated plane} is a plane $\mathcal P$ together with a pair of topologically transverse foliations $\mathcal{F}^h, \mathcal{F}^v$, possibly with isolated prong singularities. We assume throughout this work that bifoliated planes have no {\em infinite horizontal rectangles}, that is, no properly embedded subset isomorphic to $[0,\infty) \times [0, 1]$ with its horizontal and vertical product foliation.