若自映射 $σ\colon \mathcal{X} \rightarrow \mathcal{X}$ 的动力学 zeta 函数具有非零收敛半径 $1/Λ$，且序列 $ \# \mathrm{Fix}(σ^k)/Λ^k $ 的 Cesàro 均值 $B$ 存在且为正，则我们证明：对长度 $\leq X$ 的一般轨道（即由素轨道生成的自由阿贝尔幺半群中的元素，等价于 $\mathcal{X}$ 中有限多重集的素轨道）之素轨道分解中素轨道个数，存在以速率 $B \log X$ 的大偏差原理，其速率函数普适，且等于均值为 1 的泊松分布的速率函数。我们还对更一般的强可加函数证明了相应的大偏差原理。证明依赖于关于一般轨道总数的渐近结果，以及一个弱形式的 Mertens 第二定理，后者本身可能具有独立意义。该理论适用于例如有限域上代数群的自同态、加性元胞自动机，以及某些环面（solenoids）的自同构。

If a self-map $σ\colon \mathcal{X} \rightarrow \mathcal{X}$ has a dynamical zeta function with nonzero radius of convergence $1/Λ$ and the Cesàro mean $B$ of $ \# \mathrm{Fix}(σ^k)/Λ^k$ exists and is positive, we show a large deviation principle for the number of prime orbits occurring in the decomposition of a general orbit of length $\leq X$ (an element of the free abelian monoid generated by the prime orbits or, equivalently, a prime orbit of a finite multiset in $\mathcal{X}$) with speed $B \log X$ and universal rate function equal to that of the Poisson distribution with unit mean. We also show a large deviation principle for more general strongly additive functions. The proof uses asymptotic results on the total number of general orbits, as well as a weak analogue of Mertens's second theorem, that may be of independent interest. The theory applies, for example, to endomorphisms of algebraic groups over finite fields, additive cellular automata, and automorphisms of some solenoids.