ON A STRUCTURE OF NON-WANDERING SET OF AN Ω-STABLE 3-DIFFEOMORPHISM POSSESSING A HYPERBOLIC ATTRACTOR

被引：0

作者：

Barinova, Marina ^{[1
]}

Pochinka, Olga ^{[1
]}

Yakovlev, Evgeniy ^{[1
]}

机构：

[1] HSE Univ, Moscow, Russia

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2024年 / 44卷 / 01期

关键词：

Hyperbolic attractor; expanding attractor; omega-stable diffeomor-phism; A-system; orientable attractor; CLASSIFICATION;

D O I：

10.3934/dcds.2023094

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper belongs to a series of papers devoted to the study of the structure of the non-wandering set of an A-diffeomorphism. We study such set NW(f) for an omega-stable diffeomorphism f, given on a closed connected 3 manifold M3. Namely, we prove that if all basic sets in NW(f) are trivial except attractors, then every non-trivial attractor is either one-dimensional non-orientable or two-dimensional expanding.

引用

页数：17

共 30 条

[1] Topological structure of non-wandering set of a graph map
Gu, RB
Sun, TX
Zheng, TT
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2005, 21 (04) : 873 - 880
[2] Topological Structure of Non-wandering Set of a Graph Map
Rong Bao GU School of Finance
ActaMathematicaSinica(EnglishSeries), 2005, 21 (04) : 873 - 880
[3] Scenario of a Simple Transition from a Structurally Stable 3-Diffeomorphism with a Two-Dimensional Expanding Attractor to a DA Diffeomorphism
V. Z. Grines
E. V. Kruglov
O. V. Pochinka
Proceedings of the Steklov Institute of Mathematics, 2020, 308 : 141 - 154
[4] Scenario of a Simple Transition from a Structurally Stable 3-Diffeomorphism with a Two-Dimensional Expanding Attractor to a DA Diffeomorphism
Grines, V. Z.
Kruglov, E. V.
Pochinka, O. V.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2020, 308 (01) : 141 - 154
[5] Non-wandering set of a continuous graph map
Rongbao Gu
Taixiang Sun
Tingting Zheng
Applied Mathematics-A Journal of Chinese Universities, 2003, 18 (4) : 477 - 481
[6] The non-wandering set of some Henon maps
Cao, YL
Mao, JM
CHAOS SOLITONS & FRACTALS, 2000, 11 (13) : 2045 - 2053
[7] NON-WANDERING SET OF A CONTINUOUS GRAPH MAP
Gu Rongbao 1
AppliedMathematics:AJournalofChineseUniversities, 2003, (04) : 477 - 481
[8] HYPERBOLIC NON-WANDERING SETS WITHOUT DENSE PERIODIC POINTS
KURATA, M
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1978, 54 (07) : 206 - 211
[9] CONTINUOUS MAPS OF INTERVAL WITH FINITE NON-WANDERING SET
BLOCK, L
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1978, 240 (JUN) : 221 - 230
[10] The structure of non-wandering sets of interval maps
Liu, GP
Ye, XD
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON DIFFERENTIAL EQUATIONS AND COMPUTATIONAL SIMULATIONS, 2000, : 416 - 421

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