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Nonlocally maximal and premaximal hyperbolic sets. / Fisher, T.; Petty, T.; Тихомиров, Сергей Борисович.

Contemporary Mathematics. American Mathematical Society, 2017. p. 83-99 (Contemporary Mathematics; Vol. 692).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

Harvard

Fisher, T, Petty, T & Тихомиров, СБ 2017, Nonlocally maximal and premaximal hyperbolic sets. in Contemporary Mathematics. Contemporary Mathematics, vol. 692, American Mathematical Society, pp. 83-99. https://doi.org/10.1090/conm/692/13914

APA

Fisher, T., Petty, T., & Тихомиров, С. Б. (2017). Nonlocally maximal and premaximal hyperbolic sets. In Contemporary Mathematics (pp. 83-99). (Contemporary Mathematics; Vol. 692). American Mathematical Society. https://doi.org/10.1090/conm/692/13914

Vancouver

Fisher T, Petty T, Тихомиров СБ. Nonlocally maximal and premaximal hyperbolic sets. In Contemporary Mathematics. American Mathematical Society. 2017. p. 83-99. (Contemporary Mathematics). https://doi.org/10.1090/conm/692/13914

Author

Fisher, T. ; Petty, T. ; Тихомиров, Сергей Борисович. / Nonlocally maximal and premaximal hyperbolic sets. Contemporary Mathematics. American Mathematical Society, 2017. pp. 83-99 (Contemporary Mathematics).

BibTeX

@inbook{e5212f65dfbd4062bd345446f19c4f1f,
title = "Nonlocally maximal and premaximal hyperbolic sets",
abstract = "We prove that for any closed manifold of dimension 3 or greater there is an open set of smooth flows that have a hyperbolic set that is not contained in a locally maximal one. Additionally, we show that the stabilization of the shadowing closure of a hyperbolic set is an intrinsic property for premaximality. Lastly, we review some results due to Anosov that concern premaximality.",
keywords = "Hyperbolic flow, Hyperbolic sets, Isolated, Locally maximal, Premaximal",
author = "T. Fisher and T. Petty and Тихомиров, {Сергей Борисович}",
year = "2017",
month = jan,
day = "1",
doi = "10.1090/conm/692/13914",
language = "English",
series = "Contemporary Mathematics",
publisher = "American Mathematical Society",
pages = "83--99",
booktitle = "Contemporary Mathematics",
address = "United States",

}

RIS

TY - CHAP

T1 - Nonlocally maximal and premaximal hyperbolic sets

AU - Fisher, T.

AU - Petty, T.

AU - Тихомиров, Сергей Борисович

PY - 2017/1/1

Y1 - 2017/1/1

N2 - We prove that for any closed manifold of dimension 3 or greater there is an open set of smooth flows that have a hyperbolic set that is not contained in a locally maximal one. Additionally, we show that the stabilization of the shadowing closure of a hyperbolic set is an intrinsic property for premaximality. Lastly, we review some results due to Anosov that concern premaximality.

AB - We prove that for any closed manifold of dimension 3 or greater there is an open set of smooth flows that have a hyperbolic set that is not contained in a locally maximal one. Additionally, we show that the stabilization of the shadowing closure of a hyperbolic set is an intrinsic property for premaximality. Lastly, we review some results due to Anosov that concern premaximality.

KW - Hyperbolic flow

KW - Hyperbolic sets

KW - Isolated

KW - Locally maximal

KW - Premaximal

UR - http://www.scopus.com/inward/record.url?scp=85029552518&partnerID=8YFLogxK

U2 - 10.1090/conm/692/13914

DO - 10.1090/conm/692/13914

M3 - Chapter

AN - SCOPUS:85029552518

T3 - Contemporary Mathematics

SP - 83

EP - 99

BT - Contemporary Mathematics

PB - American Mathematical Society

ER -

ID: 43393070