Bundle switching in higher dimensions
arXiv:2306.14491
Abstract
Assuming it preserves an orientation of its stable bundle, any three-dimensional partially hyperbolic diffeomorphism can be used to construct a four-dimensional partially hyperbolic diffeomorphism which is dynamically incoherent. Under the same assumption, the time-one map of any three-dimensional Anosov flow can be used to construct a four-dimensional diffeomorphism which is both absolutely partially hyperbolic and dynamically incoherent. Further results hold in higher dimensions under additional assumptions.
arXiv comment23 pages, 4 figures