Analysis of stationary points and their bifurcations in the ABC flow

Abstract

Analytical expressions for coordinates of stationary points and conditions for their existence in the ABC flow are received. The type of the stationary points is shown analytically to be saddle-node. Exact expressions for eigenvalues and eigenvectors of the stability matrix are given. Behavior of the stationary points along the bifurcation lines is described.

References in corpus (7)

• Revisiting the ABC flow dynamo
• Detecting barrier to cross-jet Lagrangian transport and its destruction in a meandering flow
• Effect of dynamical traps on chaotic transport in a meandering jet flow
• Toward an asymptotic behaviour of the ABC dynamo
• Mechanism of destruction of transport barriers in geophysical jets with Rossby waves
• About existence of stationary points for the Arnold-Beltrami-Childress (ABC) flow
• Nonlinear resonances in the $ABC$-flow

Cited by in corpus (1)

• A kind of Lagrangian chaotic property of the Arnold-Beltrami-Childress flow