Quasi-periodic solutions of Hamiltonian PDEs

Massimiliano Berti

Displaying similar documents to “Quasi-periodic solutions of Hamiltonian PDEs”

Changing blow-up time in nonlinear Schrödinger equations

Rémi Carles (2003)

Journées équations aux dérivées partielles

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Solutions to nonlinear Schrödinger equations may blow up in finite time. We study the influence of the introduction of a potential on this phenomenon. For a linear potential (Stark effect), the blow-up time remains unchanged, but the location of the collapse is altered. The main part of our study concerns isotropic quadratic potentials. We show that the usual (confining) harmonic potential may anticipate the blow-up time, and always does when the power of the nonlinearity is $L^{2}$ -critical....

Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms

Viviane Baladi, Masato Tsujii (2007)

Annales de l’institut Fourier

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We study spectral properties of transfer operators for diffeomorphisms $T : X \to X$ on a Riemannian manifold $X$ . Suppose that $Ω$ is an isolated hyperbolic subset for $T$ , with a compact isolating neighborhood $V \subset X$ . We first introduce Banach spaces of distributions supported on $V$ , which are anisotropic versions of the usual space of $C^{p}$ functions $C^{p} (V)$ and of the generalized Sobolev spaces $W^{p, t} (V)$ , respectively. We then show that the transfer operators associated to $T$ and a smooth weight $g$ extend boundedly to these...

Moduli spaces for linear differential equations and the Painlevé equations

Marius van der Put, Masa-Hiko Saito (2009)

Annales de l’institut Fourier

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A systematic construction of isomonodromic families of connections of rank two on the Riemann sphere is obtained by considering the analytic Riemann–Hilbert map $R H : ℳ \to ℛ$ , where $ℳ$ is a moduli space of connections and $ℛ$ , , is a moduli space for analytic data (, ordinary monodromy, Stokes matrices and links). The assumption that the fibres of $R H$ (, the isomonodromic families) have dimension one, leads to ten moduli spaces $ℳ$ . The induced Painlevé equations are computed explicitly. Except for the...