Many intermingled basins in dimension 3

Christian Bonatti; Rafael Potrie

Many intermingled basins in dimension 3

Dynamical Systems 2017-02-06 v2

Authors: Christian Bonatti , Rafael Potrie

Abstract

We construct a diffeomorphism of $\mathbb{T}^3$ admitting any finite or countable number of physical measures with intermingled basins. The examples are partially hyperbolic with splitting $T\mathbb{T}^3 = E^{cs} \oplus E^u$ and can be made volume hyperbolic and topologically mixing.

Keywords

partially hyperbolic dynamics hyperbolic geometry hyperbolic 3-manifolds

Cite

@article{arxiv.1603.03803,
  title  = {Many intermingled basins in dimension 3},
  author = {Christian Bonatti and Rafael Potrie},
  journal= {arXiv preprint arXiv:1603.03803},
  year   = {2017}
}

Comments

20 pages, 4 figures. Some changes made after referee report. To appear in Israel J. of Math

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