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The paper is an informal report on joint work with Stefan Haller on Dynamics in relation with Topology and Spectral Geometry. By dynamics one means a smooth vector field on a closed smooth manifold; t...
It is well known, by now, that the three-dimensional non-viscous planetary geostrophic model, with vertical hydrostatic balance and horizontal Rayleigh friction, coupled to the heat diffusion and tra...
In these notes we review some recent results concerning the derivation of effective equations from first principle quantum dynamics. In particular, we discuss the derivation of the semi-relativistic...
First and foremost, I would like to thank my advisor Sarah Koch for being so generous with her time and energy.
Quasiparticle approach to dynamics of dark solitons is applied to the case of ring solitons. It is shown that the energy conservation law provides the effective equations of motion of ring dark solito...
We extend our previous result on the focusing cubic Klein-Gordon equation in three dimensions to the non-radial case, giving a complete classification of global dynamics of all solutions with energy a...
The Gentlest Ascent Dynamics     Ascent Dynamics  math       2010/11/8
Dynamical systems that describe the escape from the basins of attraction of stable invariant sets are presented and analyzed. It is shown that the stable fixed points of such dynamical systems are th...
We consider a rational system of first order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the paramet...
Dispersive averaging e ects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly.
This is the first part of our mathematical survey on the equations of motion of classical absorber electrodynamics, which shall be introduced and discussed briefly. Its basic equations of motion are t...
We consider the ordered and disordered dynamics for monolayers of rolling self-interacting par- ticles with an o -set center of mass and a non-isotropic inertia tensor. The rolling constraint is cons...
Given a locally maximal compact invariant hyperbolic set  for a C1 flow or diffeomorphism on a Riemann manifold with C1 unstable laminations, we construct an invariant continuous bundle of tangent ve...
Let T : X ! X be a compact linear (or more generally affine) operator from a Banach space into itself. For each x 2 X, the sequence of iterates T nx, n = 0, 1, · · · and its averages 1 k Pn k=0 T k...
The propagation of molecular chaos, a tool of classical kinetic theory, is generalized to apply to quantum systems of distinguishable particles. We prove that the Curie-Weiss model of ferromagnetism ...

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