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Journal of the European Mathematical Society


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Volume 10, Issue 1, 2008, pp. 1–45
DOI: 10.4171/JEMS/102

Published online: 2008-03-31

Quasi-periodic solutions of nonlinear random Schrödinger equations

Jean Bourgain[1] and Wei-Min Wang[2]

(1) Institute for Advanced Study, Princeton, United States
(2) University of Massachusetts, Amherst, United States

In this paper, let $\Sigma\subset\R^{6}$ be a compact convex hypersurface. We prove that if $\Sigma$ carries only finitely many geometrically distinct closed characteristics, then at least two of them must possess irrational mean indices. Moreover, if $\Sg$ carries exactly three geometrically distinct closed characteristics, then at least two of them must be elliptic.

Keywords: Compact convex hypersurfaces, closed characteristics, Hamiltonian systems, Morse theory, mean index identity, stability

Bourgain Jean, Wang Wei-Min: Quasi-periodic solutions of nonlinear random Schrödinger equations. J. Eur. Math. Soc. 10 (2008), 1-45. doi: 10.4171/JEMS/102