What does this research mean for the field?

The continuity property of Lyapunov exponents extends to smooth interval maps with non-flat critical points, and these exponents are uniformly integrable over entropies. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This research aims to establish the continuity of Lyapunov exponents for smooth interval maps with non-flat critical points, extending existing results from surface diffeomorphisms.

June 7, 2026Ergodic Theory and Dynamical Systems

Entropy continuity of Lyapunov exponents for non-flat one-dimensional maps

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Authors

HLHENGYI LIUniversité Paris-Saclay

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Implication

Randomized trial shows continuity of Lyapunov exponents in non-flat maps, suggesting broader applications in dynamical systems.

Key Points

This research aims to establish the continuity of Lyapunov exponents for smooth interval maps with non-flat critical points, extending existing results from surface diffeomorphisms.
Applied results from previous studies on surface diffeomorphisms to smooth interval maps.
Examined conditions under which Lyapunov exponents remain continuous despite the presence of non-flat critical points.
Assessed uniform integrability of Lyapunov exponents over varying entropies.
Demonstrated that the continuity property of Lyapunov exponents extends to non-flat critical point maps.
Proved uniform integrability of Lyapunov exponents in relation to converging entropies.
Established a stronger framework for understanding the behavior of Lyapunov exponents compared to previous studies.

Cite This Study

HENGYI LI (2026) studied this question.

synapsesocial.com/papers/6a250c687def13d035e1c8dc https://doi.org/10.1017/etds.2026.10304

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Entropy continuity of Lyapunov exponents for non-flat one-dimensional maps

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Entropy continuity of Lyapunov exponents for non-flat one-dimensional maps

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