A Dichotomy in Area-Preserving Reversible Maps

被引：2
|
作者：
Bessa, Mario [1 ]
Rodrigues, Alexandre A. P. [2 ]
机构：
[1] Univ Beira Interior, Dept Matemat, Rua Marques dAvila e Bolama, P-6201001 Covilha, Portugal
[2] Univ Porto, Ctr Matemat, Rua Campo Alegre 687, P-4169007 Oporto, Portugal
来源：
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2016年 / 15卷 / 02期
关键词：
Reversing symmetry; Area-preserving map; Closing Lemma; Elliptic point; DYNAMICAL-SYSTEMS; PERIODIC-ORBITS; CLOSING LEMMA; DIFFEOMORPHISMS; POINTS;
D O I：
10.1007/s12346-015-0155-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study R-reversible area-preserving maps f : M -> M on a two-dimensional Riemannian closed manifold M, i.e. diffeomorphisms f such that R circle f = f(-1) circle R where R : M -> M is an isometric involution. We obtain a C-1-residual subset where any map inside it is Anosov or else has a dense set of elliptic periodic orbits, thus establishing the stability conjecture in this setting. Along the paper we derive the C-1-Closing Lemma for reversible maps and other perturbation toolboxes.
引用
收藏
页码：309 / 326
页数：18
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