Temporal Dynamics in Perturbation Theory
arXiv:cond-mat/9712039 · doi:10.1016/0378-4371(95)00471-8
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.
1 file, 21 pages, RevTex, 2 tables
Cited by in corpus (38)
- Basics of Bose-Einstein Condensation
- Physics of risk and uncertainty in quantum decision making
- Self-Similar Factor Approximants
- Summation of Power Series by Self-Similar Factor Approximants
- Unified Approach to Crossover Phenomena
- Self-Similar Exponential Approximants
- Self-Similar Structures and Fractal Transforms in Approximation Theory
- Critical Indices as Limits of Control Functions
- Self-Similar Perturbation Theory
- Self-Similar Bootstrap of Divergent Series
- Information Processing by Networks of Quantum Decision Makers
- Method of self-similar factor approximants
- Renormalization Group Analysis of October Market Crashes
- Extrapolation of power series by self-similar factor and root approximants
- Optimal trap shape for a Bose gas with attractive interactions
- Weighted Fixed Points in Self-Similar Analysis of Time Series
- Self-Similar Crossover in Statistical Physics
- Calculation of critical exponents by self-similar factor approximants
- Stochastic Instability of Quasi-Isolated Systems
- Highly Accurate Critical Exponents from Self-Similar Variational Perturbation Theory
- Self-similar factor approximants for evolution equations and boundary-value problems
- Self-similar continued root approximants
- Self-Similar Extrapolation of Asymptotic Series and Forecasting for Time Series
- Classification of Possible Finite-Time Singularities by Functional Renormalization
- Booms and Crashes in Self-Similar Markets
- Principle of Pattern Selection for Nonequilibrium Phenomena
- Interplay Between Approximation Theory and Renormalization Group
- Renormalization--Group Solutions for Yukawa Potential
- Optimization of self-similar factor approximants
- Resummation Methods for Analyzing Time Series
- Self-similar Approximants of the Permeability in Heterogeneous Porous Media from Moment Equation Expansions
- New Approach to Modeling Symbiosis in Biological and Social Systems
- Functional Renormalization Prediction of Rupture
- Extrapolation of perturbation-theory expansions by self-similar approximants
- Population dynamics with nonlinear delayed carrying capacity
- Self-similar interpolation in high-energy physics
- From Asymptotic Series to Self-Similar Approximants
- Effective Summation and Interpolation of Series by Self-Similar Root Approximants