Isotropy group of Lotka-Volterra derivations

2024/12/30 by Himanshu Rewri, Surjeet Kour, Rewri, Himanshu +1
Mathematics · Medicine · #Advanced Differential Equations and Dynamical Systems #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2412.20832

Abstract

In this paper, we study the isotropy group of Lotka-Volterra derivations of K[x₁,⋯,x_n], i.e., a derivation d of the form d(x_i)=x_i(x_i-1-C_ix_i+1). If n=3 or n ≥ 5, we have shown that the isotropy group of d is finite. However, for n=4, it is observed that the isotropy group of d need not be finite. Indeed, for C_i=-1, we observed an infinite collection of automorphisms in the isotropy group of d. Moreover, for n ≥ 3, ~~and~~C_i=1, we have shown that the isotropy group of d is isomorphic to the dihedral group of order 2n.

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