Consider an ergodic measure preserving dynamical system (T, X,μ), and an observable . For the time series X _n (x) = ϕ(T ⁿ (x)), we establish limit laws for the maximum process M _n =max _k⩽n X _k in the case where ϕ is an observable maximized on a line segment, and (T, X,μ) is a hyperbolic dynamical system. Such observables arise naturally in weather and climate applications. We consider the extreme value laws and extremal indices for these observables on hyperbolic toral automorphisms, Sinai dispersing billiards and coupled expanding maps. In particular we obtain clustering and nontrivial extremal indices due to self intersection of submanifolds under iteration by the dynamics, not arising from any periodicity.

考虑一个遍历测度保留动力系统（T，X，μ）和一个 observable 。对于时间序列X _n ( x ) = ϕ ( T ⁿ ( x ))，我们建立了最大过程M _n =max _{k ⩽ n} X _{k 的}极限定律，其中ϕ是在线段上最大化的可观测量，和 ( T , X , μ ) 是一个双曲动力系统。此类可观测数据自然出现在天气和气候应用中。我们在双曲环自同构、西奈散布台球和耦合扩展图上考虑这些可观测量的极值定律和极值指数。特别是，由于动力学迭代下子流形的自相交，我们获得了聚类和非平凡的极值指数，而不是由任何周期性引起的。