Temporal dynamics in perturbation theory

V.I. Yukalov and E.P. Yukalova

Physica A: Statistical Mechanics and its Applications, 1996, vol. 225, issue 3, 336-362

Abstract: Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our attention on the stability conditions permitting to control the convergence of approximation sequences. We show that several types of mapping multipliers and Lyapunov exponents can be introduced and, respectively, several types of conditions controlling local stability can be formulated. The ideas are illustrated by calculating the energy levels of an anharmonic oscillator.

Keywords: Sequences, series and summability; Approximations and expansions; Bound states (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:225:y:1996:i:3:p:336-362

DOI: 10.1016/0378-4371(95)00471-8

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