论文标题
双曲线流的急剧大偏差
Sharp large deviations for hyperbolic flows
论文作者
论文摘要
对于双曲线流$φ_T$，我们检查了gibb的点$ W $的GIBB $ w $的$ \ int_0^t g（φ_tw）dt-a t \ in（ - e^{ - εn}，e^{ - εn}，e^{ - εn}）$ n \ at $ n \ to $ n \ to \ n \ to \ infty $ infty $ and uftty $ and $ t-iS uffty and $ t \ geq n $，这类似于局部中央限制定理。间隔$（-e^{ - εn}，e^{ - εn}）$的事实是，作为$ n \ to \ infty $的成倍收缩，导致了几个困难。在某些几何假设下，我们建立了一个急剧的较大偏差结果，并以$ c（a）ε_ne^{γ（a）t} $和速率函数$γ（a）\ leq 0。 \ to \ infty $和$ t \ geq n。$
For hyperbolic flows $φ_t$ we examine the Gibbs measure of points $w$ for which $$\int_0^T G(φ_t w) dt - a T \in (- e^{-εn}, e^{- εn})$$ as $n \to \infty$ and $T \geq n$, provided $ε> 0$ is sufficiently small. This is similar to local central limit theorems. The fact that the interval $(- e^{-εn}, e^{- εn})$ is exponentially shrinking as $n \to \infty$ leads to several difficulties. Under some geometric assumptions we establish a sharp large deviation result with leading term $C(a) ε_n e^{γ(a) T}$ and rate function $γ(a) \leq 0.$ The proof is based on the spectral estimates for the iterations of the Ruelle operators with two complex parameters and on a new Tauberian theorem for sequence of functions $g_n(t)$ having an asymptotic as $ n \to \infty$ and $t \geq n.$
