# Entropy of logarithmic modes

#### Dr Suresh Eswarathasan (Dalhousie University, Halifax, Canada) will present his research in Analysis.

Consider $(M,g)$ a hyperbolic surface without boundary and its semiclassical Laplace-Beltrami operator $-\hbar^2 \Delta$.  It was shown that for sequences of $-\hbar^2 \Delta$ eigenfunctions (with energy 1, say) and corresponding semiclassical measure $\mu_{sc}$, the Kolmogorov-Sinai entropy of $\mu_{sc}$ is bounded below by 1/2.  In this talk, we study thesemiclassical measures $\mu_{sc}$ of $\epsilon$-logarithmic modes, which are sums of eigenfunctions spectrally supported in intervals of width $\epsilon \frac{\h}{|\log \h|}$.

We show that the lower bound for the Kolmogorov-Sinai entropy of the corresponding $\mu_{sc}$s generalizes that of Ananthamaran-Koch-Nonnenmacher.  In particular, our entropy bound depends continuously on the width parameter $\epsilon$ and recovers the 1/2 bound when $\epsilon=o(1)$.

The talks are held using zoom. Anyone interested in attending (outside the School of Mathematics) should email Ben Sharp at b.g.sharp@leeds.ac.uk to request zoom coordinates

#### Related events

See all School of Mathematics events