Abstract
Various physical problems are characterized by the presence of a small disturbance which, because of being active over a long time, has a non-negligible cumulative effect. For example, the effect of a small damping force over many periods of oscillation is to produce a decay in the amplitude of a linear oscillator. A fancier example having the same physical and mathematical features is the motion of a satellite around the earth, where the dominant force is a spherically symmetric gravitational field. If this were the only force acting on the satellite the motion would (for sufficiently low energies) be periodic. The presence of a thin atmosphere, a slightly non-spherical earth, a small moon, a distant sun, etc. all produce small but cumulative effects which after a sufficient number of orbits drastically alter the nature of the motion.
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Kevorkian, J., Cole, J.D. (1981). Multiple-Variable Expansion Procedures. In: Perturbation Methods in Applied Mathematics. Applied Mathematical Sciences, vol 34. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4213-8_3
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