A counterexample to the "composition conjecture"

Real analytic counterexample to the freeness conjecture

We provide a counterexample to P.~Olver's freeness conjecture for $C^ω$ transformations.

A Computational Method for Large Scale Searching of Counterexamples to the Strong Coincidence Conjecture

In this short note we report on results on a computational search for a counterexample to the strong coincidence conjecture. In particular, we discuss the method used so that further searches can be conducted.

A C^2-smooth counterexample to the Hamiltonian Seifert conjecture in R^4

We give a detailed construction of a proper C^2-smooth function on R^4 such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as a C^2-smooth counterexample to the Hamiltonian Seifert conjecture in dimension four.

On the construction of a C^2-counterexample to the Hamiltonian Seifert Conjecture in R^4

We outline the construction of a proper C^2-smooth function on R^4 such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as a C^2-smooth counterexample to the Hamiltonian Seifert conjecture in dimension four.

Minkowski唯一性猜想的反例及正特征中的质量逃逸

Counterexamples to Minkowski's Uniqueness Conjecture and Escape of Mass in Positive Characteristic

本文构造紧致A轨道，证明正特征下Minkowski唯一性猜想存在无穷多反例，并揭示这些轨道及更大序列轨道必然发生完全质量逃逸。

The Deift Conjecture: A Program to Construct a Counterexample

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.