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

页码：309 / 326

页数：18

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