具有双曲吸引子的稳定3-微分同胚的非游走集结构

IF 1.1 3区数学 Q1 MATHEMATICS

Discrete and Continuous Dynamical Systems Pub Date : 2023-05-31 DOI:10.3934/dcds.2023094

M. Barinova, O. Pochinka, E. Yakovlev

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引用次数: 0

摘要

本文是研究a -微分同构的非游走集结构的系列论文之一。研究了闭连通3流形M^3$上的稳定微分同态f$的集NW(f)$。即，我们证明了如果$NW(f)$中除吸引子外的所有基本集合都是平凡的，则每个非平凡吸引子要么是一维不可定向的，要么是二维展开的。

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On a structure of non-wandering set of an $ \Omega $-stable 3-diffeomorphism possessing a hyperbolic attractor

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 $M^3$. 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.

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来源期刊

Discrete and Continuous Dynamical Systems 数学-数学

CiteScore

2.50

自引率

0.00%

发文量

175

审稿时长

6 months

期刊介绍： DCDS, series A includes peer-reviewed original papers and invited expository papers on the theory and methods of analysis, differential equations and dynamical systems. This journal is committed to recording important new results in its field and maintains the highest standards of innovation and quality. To be published in this journal, an original paper must be correct, new, nontrivial and of interest to a substantial number of readers.