Related Experiment Video
Updated: Aug 16, 2026

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
Published on: February 27, 2016
Adiabatic chaos in a two-dimensional mapping
D. L. Vainshtein1, A. A. Vasiliev, A. I. Neishtadt
1Space Research Institute, Russian Academy of Sciences, 84/32 Profsoyuznaya St., 117810, Moscow, Russia.
Abstract:
A close to identity symplectic mapping describing the dynamics of a charged particle in the field of an infinitely wide packet of electrostatic waves is studied. A region of chaotic dynamics, whose width is large for an arbitrarily small deviation of the mapping from the identity, exists on the phase cylinder. This is explained by the quasirandom change occurring in an adiabatic invariant of the problem when the phase trajectory crosses a resonance curve. An asymptotic formula is derived for the jump in the adiabatic invariant. The width of the chaos region and the density of the set of invariant curves near the boundary of the chaos region are estimated. (c) 1996 American Institute of Physics.
Related Concept Videos
Collisions in Multiple Dimensions: Problem Solving
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Two-Dimensional Force System
The Entropy as a State Function
Graphs of Two-Variable Functions
Level Curves and Contour Maps

