Generic dynamics of 4-dimensional C2 Hamiltonian systems

被引：22

作者：

Bessa, Mario ^{[1
]}

Dias, Joao Lopes ^{[2
]}

机构：

[1] Univ Porto, Ctr Matemat, P-4169007 Oporto, Portugal

[2] Univ Tecn Lisboa, ISEG, Dept Matemat, P-1200781 Lisbon, Portugal

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2008年 / 281卷 / 03期

关键词：

D O I：

10.1007/s00220-008-0500-y

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study the dynamical behaviour of Hamiltonian flows defined on 4-dimensional compact symplectic manifolds. We find the existence of a C-2-residual set of Hamiltonians for which there is an open mod 0 dense set of regular energy surfaces each either being Anosov or having zero Lyapunov exponents almost everywhere. This is in the spirit of the Bochi-Mane dichotomy for area-preserving diffeomorphisms on compact surfaces [2] and its continuous-time version for 3-dimensional volume-preserving flows [1].

引用

页码：597 / 619

页数：23

共 17 条

[1]

[Anonymous], 2004, ADV DYNAMICAL SYSTEM

[2] The Lyapunov exponents of generic zero divergence three-dimensional vector fields [J].