Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers
Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers
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DOI：
10.4007/annals.2004.160.375
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发表时间：
2004-09
影响因子：
4.9
通讯作者：
Carlos Morales Rojas;M. Pacifico;E. Pujals
中科院分区：
文献类型：
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作者：
Carlos Morales Rojas;M. Pacifico;E. Pujals
受洛伦兹显著的混沌流的启发，在本文中我们描述了闭三维流形上具有奇点的所有\(C^1\)鲁棒传递集的结构：它们是具有体积扩张中心方向的部分双曲的，并且要么是吸引子要么是排斥子。特别地，闭三维流形上具有奇点的任何\(C^1\)鲁棒吸引子总是具有一个不变叶状结构，其叶被流正向收缩，并且在每个轨道上都有正的李雅普诺夫指数，这表明任何\(C^1\)鲁棒吸引子都类似于几何洛伦兹吸引子。
Inspired by Lorenz’ remarkable chaotic flow, we describe in this paper the structure of all C 1 robust transitive sets with singularities for flows on closed 3-manifolds: they are partially hyperbolic with volume-expanding central direction, and are either attractors or repellers. In particular, any C 1 robust attractor with singularities for flows on closed 3-manifolds always has an invariant foliation whose leaves are forward contracted by the flow, and has positive Lyapunov exponent at every orbit, showing that any C 1 robust attractor resembles a geometric Lorenz attractor.