Henri Epstein

A global attracting set for the Kuramoto-Sivashinsky equation

AbstractNew bounds are given for the L2-norm of the solution of the Kuramoto-Sivashinsky equation

Analyticity for the Kuramoto-Sivashinsky equation

\partial _t U(x,t) = - (\partial _x^2 + \partial _x^4 )U(x,t) - U(x,t)\partial _x U(x,t)

New proofs of the existence of the Feigenbaum functions

, for initial data which are periodic with periodL. There is no requirement on the antisymmetry of the initial data. The result is

Perturbations of Geodesic Flows on Surfaces of Constant Negative Curvature and their Mixing Properties

\mathop {\lim \sup }\limits_{t \to \infty } \left\| {U( \cdot ,t)} \right\|_2 \leqslant const. L^{8/5}

Fixed points of composition operators. II

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Analyticity properties of the Feigenbaum function

In the framework of the ℒ.l.Z. formalism, the crossing property is proved on the mass shell for amplitudes involving two incoming and two outgoing stable particles with arbitrary masses. Any couple of physical regions in the (s, t, u)-plane corresponding to crossed processes are shown to be connected by a certain domain of analyticity. For every negative value oft, the amplitude is analytic in the cuts-plane outside of a large circle.