Abstract
We propose a new method for constructing partially hyperbolic diffeomorphisms on closed manifolds. As a demonstration of the method we show that there are simply connected closed manifolds that support partially hyperbolic diffeomorphisms. Laying aside many surgery constructions of 3-dimensional Anosov flows, these are the first new examples of manifolds which admit partially hyperbolic diffeomorphisms in the past forty years.
Funding Statement
The first author was partially supported by NSF grant DMS-1266282. The second author was partially supported by NSF grant DMS-1206622. The last author was partially supported by NSF grant DMS-1201326. A. Gogolev would also like to acknowledge the excellent working environment provided by the Institute for Mathematical Sciences at Stony Brook University.
Citation
Andrey Gogolev. Pedro Ontaneda. Federico Rodriguez Hertz. "New partially hyperbolic dynamical systems I." Acta Math. 215 (2) 363 - 393, 2015. https://doi.org/10.1007/s11511-016-0135-3
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