We obtain a exponential large deviation upper bound for continuousobservables on suspension semiflows over a non-uniformly expanding basetransformation with non-flat singularities and/or discontinuities, where theroof function defining the suspension behaves like the logarithm of thedistance to the singular/discontinuous set of the base map. To obtain thisupper bound, we show that the base transformation exhibits exponential slowrecurrence to the singular set. The results are applied to semiflows modelingsingular-hyperbolic attracting sets of $C^2$ vector fields. As corollary of themethods we obtain result on the existence of physical measure for classes ofpiecewise $C^{1+}$ expanding maps of the interval with singularities anddiscontinuities. We are also able to obtain exponentially fast escape ratesfrom subsets without full measure.
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机译：我们在悬浮半球上以非平面奇异性和/或不连续性的悬架半圆形的悬架半脉冲结构获得指数大的偏差上限，其中定义悬架的托管功能表现得像奇异/不连续集合的数量基本地图。为了获得统一的界限，我们表明基础转换对单数集具有指数速度速度。结果应用于Semiflows型号 - 双曲线吸引$ C ^ 2 $传染媒介字段。作为HOMETHOD的必然结果，我们获得了占地面积的课程类别的物理措施的结果，其中包括奇点和奇迹分区的间隔。我们还能够在没有完整测量的情况下获得逐次快速的逃生率。
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