New partially hyperbolic dynamical systems I

Andrey Gogolev; Pedro Ontaneda; Federico Rodriguez Hertz

doi:10.1007/s11511-016-0135-3

New partially hyperbolic dynamical systems I

Andrey Gogolev
, Pedro Ontaneda
, Federico Rodriguez Hertz

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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.

Original language	English (US)
Pages (from-to)	363-393
Number of pages	31
Journal	Acta Mathematica
Volume	215
Issue number	2
DOIs	https://doi.org/10.1007/s11511-016-0135-3
State	Published - Dec 1 2015

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s11511-016-0135-3

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title = "New partially hyperbolic dynamical systems I",

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.",

author = "Andrey Gogolev and Pedro Ontaneda and Hertz, \{Federico Rodriguez\}",

note = "Funding Information: 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. Publisher Copyright: {\textcopyright} 2016, Institut Mittag-Leffler.",

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AU - Gogolev, Andrey

AU - Ontaneda, Pedro

AU - Hertz, Federico Rodriguez

N1 - Funding Information: 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. Publisher Copyright: © 2016, Institut Mittag-Leffler.

PY - 2015/12/1

Y1 - 2015/12/1

N2 - 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.

AB - 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.

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New partially hyperbolic dynamical systems I

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