The Deift Conjecture: A Program to Construct a Counterexample
Mathematical Physics
2021-11-19 v1 Analysis of PDEs
Complex Variables
Dynamical Systems
Functional Analysis
math.MP
Abstract
We describe a program to construct a counterexample to the Deift conjecture, that is, an almost periodic function whose evolution under the KdV equation is not almost periodic in time. The approach is based on a dichotomy found by Volberg and Yuditskii in their solution of the Kotani problem, which states that there exists an analytic condition that distinguishes between almost periodic and non-almost periodic reflectionless potentials with resolvent set given by a Widom domain.
Cite
@article{arxiv.2111.09345,
title = {The Deift Conjecture: A Program to Construct a Counterexample},
author = {David Damanik and Milivoje Lukić and Alexander Volberg and Peter Yuditskii},
journal= {arXiv preprint arXiv:2111.09345},
year = {2021}
}
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41 pages