# Semi-classical limits of the first eigenfunction and concentration on the recurrent sets of a dynamical system - Mathematical Physics

Semi-classical limits of the first eigenfunction and concentration on the recurrent sets of a dynamical system - Mathematical Physics - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: Dear Reader, please find the third and last part of a series of papers on thesingular perturbation of the first eigenfunction associated to a nonself-adjoint second order elliptic operators. This series started in 1999 andwe presented the early results in 2000 at Columbia University. We published twonotes in CRAS in 2001 and 2005 summarizing our results. The present papercontains the proofs of the announced theorems and many open questions. We triedto publish these results in the the top tier of mathematical journals Annals,Acta, Duke

. but our results were not deemed sufficiently interesting forthem and probably not trendy enough. Some of you may like this work, so here itis. Best Regards, Ivan and David.We study the semi-classical limits of the first eigenfunction of a positivesecond order operator on a compact Riemannian manifold, when the diffusionconstant $\epsilon$ goes to zero. If the drift of the diffusion is given by aMorse-Smale vector field $b$, the limits of the eigenfunctions concentrate onthe recurrent set of $b$. A blow-up analysis enables us to find the mainproperties of the limit measures on a recurrent set.

Autor: David Holcman 1, Ivan Kupka 2 1 Weizmann Institute of Science, department of Mathematics, Rehovot, Israel. 2 Department of Mathem

Fuente: https://arxiv.org/