Entropy of logarithmic modes

Suresh Eswarathasan

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arXiv · 2102.13528

Entropy of logarithmic modes

Suresh Eswarathasan

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Abstract

Let $(M,g)$ be a compact, boundaryless, Riemannian manifold whose geodesic flow on its unit sphere bundle is Anosov. Consider the (semiclassical) Laplace-Beltrami operator on $M$. Let $\epsilon >0$. We study the semiclassical measures $\mu_{sc}$ of quasimodes spectrally supported in intervals of width $\epsilon \frac{h}{|\log h|}$, a critical-type regime when considering ``delocalization". We derive a lower bound for the Kolmogorov-Sinai entropy of $\mu_{sc}$ that depends explicitly on $\epsilon$, in the spirit of that given by Ananthamaran-Koch-Nonnenmacher.

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BibTeX RIS

Suresh Eswarathasan. 2021-02-26. Entropy of logarithmic modes. https://arxiv.org/abs/2102.13528

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