论文标题
块状裂解系统的投射空间的固定概率措施
Stationary probability measures on projective spaces for block-Lyapunov dominated systems
论文作者
论文摘要
给定有限维真实矢量空间$ v $，$ \ operatatOrname {pgl}（v）$和$μ$ $ $ invariant子空间$ w $，在块 - lyapunov的收缩假设下，我们提出了升降机的存在和独特性，$ p（v）\ p（v）\ setminus p（w） $ P（v/w）$。在另一个方向上，即在Block-Lyapunov扩展下，我们证明，仅当仅当$ W $中未包含的子空间$ w'稳定的$ w'稳定的$ w'稳定的$ p（v/w）$上的固定措施才有升力，并且比$ w cap w \ cap w'$更快地增长。这些完善了对Furstenberg，Kifer和Hennion给出的投影空间的固定概率度量的描述，并在相同的假设下扩展了Aoun，Benoist，Benoist，Bruère，Guivarc'H等相应的结果。
Given a finite-dimensional real vector space $V$, a probability measure $μ$ on $\operatorname{PGL}(V)$ and a $μ$-invariant subspace $W$, under a block-Lyapunov contraction assumption, we prove existence and uniqueness of lifts to $P(V)\setminus P(W)$ of stationary probability measures on the quotient $P(V/W)$. In the other direction, i.e. under block-Lyapunov expansion, we prove that stationary measures on $P(V/W)$ have lifts if any only if the group generated by the support of $μ$ stabilizes a subspace $W'$ not contained in $W$ and exhibiting a faster growth than on $W \cap W'$. These refine the description of stationary probability measures on projective spaces as given by Furstenberg, Kifer and Hennion, and under the same assumptions, extend corresponding results by Aoun, Benoist, Bruère, Guivarc'h, and others.
