On toral eigenfunctions and the random wave model
نویسندگان
چکیده
منابع مشابه
On the nodal sets of toral eigenfunctions
We study the nodal sets of eigenfunctions of the Laplacian on the standard d-dimensional flat torus. The question we address is: Can a fixed hypersurface lie on the nodal sets of eigenfunctions with arbitrarily large eigenvalue? In dimension two, we show that this happens only for segments of closed geodesics. In higher dimensions, certain cylindrical sets do lie on nodal sets corresponding to ...
متن کاملRestriction of Toral Eigenfunctions to Hypersurfaces
Let T = R/Z be the d-dimensional flat torus. We establish for d = 2, 3 uniform upper and lower bounds on the restrictions of the eigenfunctions of the Laplacian to smooth hyper-surfaces with non-vanishing curvature.
متن کاملRestriction of Toral Eigenfunctions to Hypersurfaces and Nodal Sets
We give uniform upper and lower bounds for the L norm of the restriction of eigenfunctions of the Laplacian on the three-dimensional standard flat torus to surfaces with non-vanishing curvature. We also present several related results concerning the nodal sets of eigenfunctions.
متن کاملQuenched Clt for Random Toral Automorphism
We establish a quenched Central Limit Theorem (CLT) for a smooth observable of random sequences of iterated linear hyperbolic maps on the torus. To this end we also obtain an annealed CLT for the same system. We show that, almost surely, the variance of the quenched system is the same as for the annealed system. Our technique is the study of the transfer operator on an anisotropic Banach space ...
متن کاملLinearisation of conservative toral homeomorphisms and toral flows
We prove an analogue of Poincaré’s classification of circle homeomorphisms for conservative homeomorphisms of the two-torus with unique rotation vector and a certain bounded mean motion property. In particular, this provides an equivalent characterisation of the semi-conjugacy class of an irrational rotation within the space of conservative toral homeomorphisms. For minimal toral homeomorphisms...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2014
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-014-1037-z