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Temporal dynamics in perturbation theory

Author

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  • Yukalov, V.I.
  • Yukalova, E.P.

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.

Suggested Citation

  • Yukalov, V.I. & Yukalova, E.P., 1996. "Temporal dynamics in perturbation theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 225(3), pages 336-362.
    • Handle: RePEc:eee:phsmap:v:225:y:1996:i:3:p:336-362
    DOI: 10.1016/0378-4371(95)00471-8
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    References listed on IDEAS

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    1. Yukalov, V.I. & Yukalova, E.P., 1993. "Self-similar approximations for thermodynamic potentials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 198(3), pages 573-592.
    2. Yukalov, V.I. & Yukalova, E.P., 1994. "Higher orders of self-similar approximations for thermodynamic potentials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 206(3), pages 553-580.
    3. Yukalov, V.I., 1986. "Effective Hamiltonians for systems with mixed symmetry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 136(2), pages 575-587.
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    Citations

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    Cited by:

    1. Simon Gluzman & Vyacheslav I. Yukalov, 2015. "Effective Summation and Interpolation of Series by Self-Similar Root Approximants," Mathematics, MDPI, vol. 3(2), pages 1-17, June.
    2. Yukalov, V.I. & Sornette, D. & Yukalova, E.P., 2009. "Nonlinear dynamical model of regime switching between conventions and business cycles," Journal of Economic Behavior & Organization, Elsevier, vol. 70(1-2), pages 206-230, May.

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