Teoretičeskaâ i matematičeskaâ fizika, Tome 66 (1986) no. 1, pp. 146-149
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A. N. Vasil'ev; M. A. Guzev. Simple proof that an adiabatic invariant is conserved to exponential accuracy over a complete interval of development. Teoretičeskaâ i matematičeskaâ fizika, Tome 66 (1986) no. 1, pp. 146-149. http://geodesic.mathdoc.fr/item/TMF_1986_66_1_a10/
@article{TMF_1986_66_1_a10,
author = {A. N. Vasil'ev and M. A. Guzev},
title = {Simple proof that an adiabatic invariant is conserved to exponential accuracy over a~complete interval of development},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {146--149},
year = {1986},
volume = {66},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1986_66_1_a10/}
}
TY - JOUR
AU - A. N. Vasil'ev
AU - M. A. Guzev
TI - Simple proof that an adiabatic invariant is conserved to exponential accuracy over a complete interval of development
JO - Teoretičeskaâ i matematičeskaâ fizika
PY - 1986
SP - 146
EP - 149
VL - 66
IS - 1
UR - http://geodesic.mathdoc.fr/item/TMF_1986_66_1_a10/
LA - ru
ID - TMF_1986_66_1_a10
ER -
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%A A. N. Vasil'ev
%A M. A. Guzev
%T Simple proof that an adiabatic invariant is conserved to exponential accuracy over a complete interval of development
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1986
%P 146-149
%V 66
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1986_66_1_a10/
%G ru
%F TMF_1986_66_1_a10
The Bogolyubov–Zubarev fast-phase method [1] is used to give a simple proof of the following well-known proposition [2]: when a perturbation is switched on and off smoothly, the total increment of the adiabatic invariant (the action) for one-dimensional periodic motion in a slowly varying potential is a quantity less than any power of $\alpha$, where $\alpha$ is a parameter that characterizes the rate of change of the potential.
