论文标题
纤维部分双曲系统的双曲线和刚度
Hyperbolicity and Rigidity for Fibred Partially Hyperbolic Systems
论文作者
论文摘要
每个具有二维中心（1）具有两个不同中心的lyapunov指数的部分具有二维中心的部分固定纤维纤维纤维系统，或（2）表现出与中心叶子的连续线场（或一对线场）的不变连续线场（或一对线场），或者（3）在中心叶子的下方构造和（3）的中心叶子的连续结构上都在动力学和不变的动力学下，并且是一个稳定的范围。最后两个替代方案对中心叶的拓扑具有强大的限制：（2）只能发生在摩ri上，对于（3）中心叶子必须是托里或球体。此外，在某些其他条件下，这些地图在拓扑结合特定代数模型的意义上是刚性的。当系统为符号（1）时，意味着中心的lyapunov指数为非零，因此系统是（不均匀）双曲线。
Every volume-preserving centre-bunched fibred partially hyperbolic system with 2-dimensional centre either (1) has two distinct centre Lyapunov exponents, or (2) exhibits an invariant continuous line field (or pair of line fields) tangent to the centre leaves, or (3) admits a continuous conformal structure on the centre leaves invariant under both the dynamics and the stable and unstable holonomies. The last two alternatives carry strong restrictions on the topology of the centre leaves: (2) can only occur on tori, and for (3) the centre leaves must be either tori or spheres. Moreover, under some additional conditions, such maps are rigid, in the sense that they are topologically conjugate to specific algebraic models. When the system is symplectic (1) implies that the centre Lyapunov exponents are non-zero, and thus the system is (non-uniformly) hyperbolic.
