Acta Mathematica

New partially hyperbolic dynamical systems I

Andrey Gogolev, Pedro Ontaneda, and Federico Rodriguez Hertz

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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.

Note

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.

Article information

Source
Acta Math., Volume 215, Number 2 (2015), 363-393.

Dates
Received: 21 May 2014
Revised: 20 October 2015
First available in Project Euclid: 30 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485802456

Digital Object Identifier
doi:10.1007/s11511-016-0135-3

Mathematical Reviews number (MathSciNet)
MR3455236

Zentralblatt MATH identifier
1357.37048

Rights
2016 © Institut Mittag-Leffler

Citation

Gogolev, Andrey; Ontaneda, Pedro; Hertz, Federico Rodriguez. New partially hyperbolic dynamical systems I. Acta Math. 215 (2015), no. 2, 363--393. doi:10.1007/s11511-016-0135-3. https://projecteuclid.org/euclid.acta/1485802456


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