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arXiv · 2511.15662

Normal distribution of Lyapunov exponents of periodic orbits for expanding circle maps

Kostiantyn Drach·Zhi Fu·Vadim Kaloshin·Zhiqiang Li·Carlangelo Liverani
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Abstract

For a smooth expanding circle map, we show that the empirical distribution of Lyapunov exponents of periodic points of any fixed period is close to normal, with an error that decreases as the period grows. This establishes a version of the Central Limit Theorem for such finite periodic orbits.

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Kostiantyn Drach, Zhi Fu, Vadim Kaloshin, Zhiqiang Li, Carlangelo Liverani. 2025-11-19. Normal distribution of Lyapunov exponents of periodic orbits for expanding circle maps. https://arxiv.org/abs/2511.15662

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