Growth function for an n-valued dynamics

2023/09/06 by M. Chirkov, Chirkov, M.
Mathematics · #Differential Equations and Boundary Problems #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2309.14251

openalex publication_date 2023/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article answers the question of V.M. Buchstaber about the growth function of a particular n-valued group. This question is closely related to discrete integrable systems. In this paper, we will find a formula for the growth function in the case when n is prime. In addition, we will prove a polynomial asymptotic estimate for the growth function in the general case. Finally, we will pose new problems and hypotheses about growth functions.

Related

• Cayley graphs and their growth functions for multivalued groups
• Representation Growth for Linear Groups
• Milnor's Problem on the Growth of Groups and its Consequences
• Rate of growth of random analytic functions, with an application to linear dynamics
• The growth of the first non-Euclidean filling function of the quaternionic Heisenberg Group