Repulsion and quantization in almost - harmonic maps , and asymptotics of the harmonic map flow

bubbling of almost - harmonic maps between 2 - spheres at points of zero energy density ∗

We show that bubbling of almost-harmonic maps between 2-spheres has very different behaviour depending on whether or not bubbles develop at points in the domain at which the energy density of the body map is zero. We also see that this translates into different behaviour for the harmonic map flow. In [11] we obtained results, assuming nonzero bubble point density for certain bubbles, forcing th...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Singularities of Harmonic Maps

This article surveys research on the existence, structure, behavior, and asymptotics of singularities of harmonic maps.

Energy Quantization for Harmonic Maps

In this paper we establish the higher-dimensional energy bubbling results for harmonic maps to spheres. We have shown in particular that the energy density of concentrations has to be the sum of energies of harmonic maps from the standard 2dimensional spheres. The result also applies to the structure of tangent maps of stationary harmonic maps at either a singularity or infinity. 0. Introductio...

Periodic orbit quantization of chaotic maps by harmonic inversion

A method for the semiclassical quantization of chaotic maps is proposed, which is based on harmonic inversion. The power of the technique is demonstrated for the baker’s map as a prototype example of a chaotic map. The harmonic inversion method for signal processing [1,2] has proven to be a powerful tool for the semiclassical quantization of chaotic as well as integrable dynamical systems [3–5]...