Many intermingled basins in dimension 3

Christian Bonatti (1) , Rafael Potrie (2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 CMAT - Centro de Matemática [Montevideo]

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.

Domaines: Systèmes dynamiques [math.DS]

Christian Bonatti, Rafael Potrie. Many intermingled basins in dimension 3. Israel Journal of Mathematics, 2018, 224 (1), pp.293-314. ⟨10.1007/s11856-018-1648-6⟩. ⟨hal-01801340⟩