关于沿 $E^{cu}$ 的正Lyapunov指数与部分双曲系统的非一致扩张性
动力系统
2024-06-18 v3 数学物理
微分几何
math.MP
摘要
本文考虑任意维紧黎曼流形上容许支配分裂 的 微分同胚。我们证明，若沿 的Lyapunov指数对Lebesgue几乎处处为正，则在协循环 在一个遍历Lyapunov极大可观测测度的支撑上具有指标1的支配分裂的假设下，映射 沿 是非一致扩张的。由此，对于容许支配分裂 的 微分同胚映射 ，在 对Lebesgue几乎处处具有非零Lyapunov指数且协循环 在一个遍历Lyapunov极大可观测测度的支撑上具有指标1的支配分裂的假设下，存在一个物理SRB测度。
引用
@article{arxiv.2112.11149,
title = {On positive Lyapunov exponents along $E^{cu}$ and non-uniformly expanding for partially hyperbolic systems},
author = {Reza Mohammadpour},
journal= {arXiv preprint arXiv:2112.11149},
year = {2024}
}
备注
V3: A few corrections were made. V2: Minor mistakes were corrected, the title was changed, and the article was reorganized. The main result was proven under the assumption that the cocycle $Df_{|E^{cu}(f)}^{-1}$ had a dominated splitting with index 1 on the support of an ergodic Lyapunov maximizing observable measure