Capacity of the α-Brjuno-Rüssmann set

2025/10/18 by Nurali Akramov, Akramov, Nurali
Mathematics · #11J70 #28A75 #31A15 #37F50 #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2510.16369

openalex publication_date 2025/10/18 · openalex created_date 2025/10/22 · openalex updated_date 2026/07/28

Abstract

In this work, we prove that the complement of the Brjuno set B has a zero capacity with respect to the kernel k¹_σ(z,ξ)=ln²|z-ξ||lnln(e+(1)/(|z-ξ|))|^σ for anyσ> 2. Similarly, the complement of the Perez-Marco set PM has a zero capacity with respect to the kernel k²_σ(z,ξ) = ln²ln(e+\frac1 | z - ξ|)⋅ln^σlnln(e³+\frac1 | z - ξ|) for any σ>2.

Citations

• A Diophantine duality applied to the KAM and Nekhoroshev theorems

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