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Partially hyperbolic diffeomorphisms of 3-manifolds with Abelian fundamental groups. / Burago, Dmitri; Ivanov, Sergei.

In: Journal of Modern Dynamics, Vol. 2, No. 4, 01.12.2008, p. 541-580.

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

Harvard

Burago, D & Ivanov, S 2008, 'Partially hyperbolic diffeomorphisms of 3-manifolds with Abelian fundamental groups', Journal of Modern Dynamics, vol. 2, no. 4, pp. 541-580. https://doi.org/10.3934/jmd.2008.2.541

APA

Burago, D., & Ivanov, S. (2008). Partially hyperbolic diffeomorphisms of 3-manifolds with Abelian fundamental groups. Journal of Modern Dynamics, 2(4), 541-580. https://doi.org/10.3934/jmd.2008.2.541

Vancouver

Burago D, Ivanov S. Partially hyperbolic diffeomorphisms of 3-manifolds with Abelian fundamental groups. Journal of Modern Dynamics. 2008 Dec 1;2(4):541-580. https://doi.org/10.3934/jmd.2008.2.541

Author

Burago, Dmitri ; Ivanov, Sergei. / Partially hyperbolic diffeomorphisms of 3-manifolds with Abelian fundamental groups. In: Journal of Modern Dynamics. 2008 ; Vol. 2, No. 4. pp. 541-580.

BibTeX

@article{3f0edc20cac147fc81f39ce6c7681031,
title = "Partially hyperbolic diffeomorphisms of 3-manifolds with Abelian fundamental groups",
abstract = "We present the first known nontrivial topological obstructions to the existence of partially hyperbolic diffeomorphisms. In particular, we show that there are no partially hyperbolic diffeomorphisms on the 3-sphere. More generally, we show that for a partially hyperbolic diffeomorphismof a 3-manifoldwith an Abelian fundamental group, the induced action in the first homology group is partially hyperbolic. This improves the results of [4] by dropping the assumption of dynamical coherence.",
keywords = "Dynamical coherence, Partially hyperbolic diffeomorphism, Quasi-isometric leaves, Stable unstable center distributions and foliations",
author = "Dmitri Burago and Sergei Ivanov",
year = "2008",
month = dec,
day = "1",
doi = "10.3934/jmd.2008.2.541",
language = "English",
volume = "2",
pages = "541--580",
journal = "Journal of Modern Dynamics",
issn = "1930-5311",
publisher = "American Institute of Mathematical Sciences",
number = "4",

}

RIS

TY - JOUR

T1 - Partially hyperbolic diffeomorphisms of 3-manifolds with Abelian fundamental groups

AU - Burago, Dmitri

AU - Ivanov, Sergei

PY - 2008/12/1

Y1 - 2008/12/1

N2 - We present the first known nontrivial topological obstructions to the existence of partially hyperbolic diffeomorphisms. In particular, we show that there are no partially hyperbolic diffeomorphisms on the 3-sphere. More generally, we show that for a partially hyperbolic diffeomorphismof a 3-manifoldwith an Abelian fundamental group, the induced action in the first homology group is partially hyperbolic. This improves the results of [4] by dropping the assumption of dynamical coherence.

AB - We present the first known nontrivial topological obstructions to the existence of partially hyperbolic diffeomorphisms. In particular, we show that there are no partially hyperbolic diffeomorphisms on the 3-sphere. More generally, we show that for a partially hyperbolic diffeomorphismof a 3-manifoldwith an Abelian fundamental group, the induced action in the first homology group is partially hyperbolic. This improves the results of [4] by dropping the assumption of dynamical coherence.

KW - Dynamical coherence

KW - Partially hyperbolic diffeomorphism

KW - Quasi-isometric leaves

KW - Stable unstable center distributions and foliations

UR - http://www.scopus.com/inward/record.url?scp=70349316116&partnerID=8YFLogxK

U2 - 10.3934/jmd.2008.2.541

DO - 10.3934/jmd.2008.2.541

M3 - Article

AN - SCOPUS:70349316116

VL - 2

SP - 541

EP - 580

JO - Journal of Modern Dynamics

JF - Journal of Modern Dynamics

SN - 1930-5311

IS - 4

ER -

ID: 50975492