Open Research Index

Positive Metric Entropy for the Standard Map at Large Parameters

OpenAI

OpenAI Mathopenai-math/Positive-Metric-Entropy-for-the-Standard-Map-at-Large-ParametersSep 23, 2026math.DSAI-generatedscore 0

We prove that the standard sine map of the two-dimensional torus has positive metric entropy with respect to normalized area for every sufficiently large positive parameter. This gives a full parameter tail, and hence answers Sinai's positive-parameter-measure conjecture affirmatively.

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