Generating positive geometric entropy from recurrent leaves

Ponce, Gabriel

doi:10.1090/proc/14101

Generating positive geometric entropy from recurrent leaves
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by Gabriel Ponce PDF

Proc. Amer. Math. Soc. 146 (2018), 4389-4404 Request permission

Abstract:

In this paper we introduce a $C^r$–perturbation procedure, with respect to the $C^r$–Epstein topology, for $C^r$–foliations by surfaces. Using this perturbation procedure we show how one can use the existence of recurrent leaves of a certain $C^r$–foliation $\mathcal F$ to obtain a foliation $\mathcal G$, $C^r$–close to $\mathcal F$ in the $C^r$–Epstein topology, which has a resilient leaf. In particular, one can take advantage of the recurrence property to construct examples of $C^r$–foliations, $C^r$–close to each other and such that one of them has a resilient leaf while the other is Riemannian (therefore has trivial dynamics).

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