# MathSciDoc: An Archive for Mathematician ∫

#### Dynamical Systemsmathscidoc:1608.11001

ArXiv, 2016.1
In this paper, we prove that the ODE system, $\dot{x}=sinz+cosy$ $\dot{y}=sinx+cosz$ $\dot{z}=siny+cosx$ whose right-hand side is the Arnold-Beltrami-Childress (ABC) flow with parameters A = B = C = 1, has periodic orbits on $(2 \pi T)^3$ with rotation vectors parallel to (1, 0, 0), (0, 1, 0), and (0, 0, 1). An application of this result is that the well-known G-equation model for turbulent combustion with this ABC flow on $R^3$ has a linear (i.e., maximal possible) flame speed enhancement rate as the amplitude of the flow grows.
Arnold-Beltrami-Childress (ABC) flow, periodic orbits, G-equation model
@inproceedings{jack2016periodic,
title={Periodic orbits of the ABC flow with $A=B=C=1$},

Jack Xin, Yifeng Yu, and Andrej Zlato. Periodic orbits of the ABC flow with $A=B=C=1$. 2016. In ArXiv. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160818094045740432224.