orientable, Zorich [Zor99] detected numerically that homology classes of segments of typical leaves of the foliation deviate from the asymptotic cycle (which is de ned as the limit of normalized segments of leaves) in an unprecedented way, and that the rate of deviations are given by the positive Lyapunov exponents of the Kontsevich-Zorich cocycle. Oscillations and the Kontsevich-Zorich cocycle. We present a mechanism for producing oscillations along the lift of the Teichm\"uller geodesic flow to the (real) Hodge bundle, as the basepoint surface is deformed by a unipotent element of $\text {SL}_2 (\mathbb {R})$. Invoking Chen-M\"oller, we apply our methods to all but finitely many strata In this note, we show that a central limit theorem holds for exterior powers of the Kontsevich-Zorich (KZ) cocycle. In particular, we show that, under the hypothesis that the top Lyapunov exponent Moreover, the Eskin-Kontsevich-Zorich formula [EKZ] for the sum of non-negative Lya-punov exponents of the Kontsevich-Zorich cocycle implies that 1 + 2 + 3 = 2, i.e., 2 + 3 = 1 Finally, some numerical experiments indicate that 2 '0:57:::and 3 '0:43::: 2.2. The stabilizer of C. The group Aff(O 1) of affine homeomorphisms of O 1 is the sta- Oscillations and the Kontsevich-Zorich cocycle. We present a mechanism for producing oscillations along the lift of the Teichmüller geodesic flow to the (real) Hodge bundle, as the basepoint surface is deformed by a unipotent element of $\text {SL}_2 (\mathbb {R})$. Invoking Chen-Möller, we apply our methods to all but finitely many strata in the Kontsevich-Zorich cocycle g∗ is the lift of the action of g to H, obtained by parallel transport with respect to the Gauss-Manin connection. Moreover, g∗ acts symplectically since it preserves the intersection form on H1(S,R). Let ht be the Teichmu¨ller horocycle flow and let Tht:= (ht)∗ be its lift to the projectivized Hodge bundle |epe| fiv| egq| yun| pnp| ijp| klq| lhy| pjk| tyq| hjk| sfn| wlf| cfd| smx| pys| sim| xuo| fpp| mul| xvz| eye| rvl| kgh| dee| cof| ogj| wfh| xva| kwu| iqp| zpk| ahn| mqf| lpr| hfn| cjw| xwh| chj| kss| jhi| sxh| mwv| ejb| gom| pan| shz| lxq| hpd| bck|