Asymptotics in dynamics, geometry and PDEs ; Generalized by Costin O., et al. (eds.)

By Costin O., et al. (eds.)

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Extra resources for Asymptotics in dynamics, geometry and PDEs ; Generalized borel summation. / Vol. I

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4 Summary and discussion The relationship between quantum mechanics and classical mechanics is subtle. Quantum mechanics is essentially wavelike; probability amplitudes are described by a wave equation and physical observations involve such wavelike phenomena as interference patterns and nodes. In contrast, classical mechanics describes the motion of particles and exhibits none of these wavelike features. Nevertheless, there is a deep connection between quantum mechanics and complex classical mechanics.

2 The short and long chains behind nur/mur . . 3 The nur transform . . . . . . . . 4 Expressing nur in terms of nir . . . . . 5 The mur transform . . . . . . . . 6 Translocation of the nur transform . . . . 7 Removal of the ingress factor . . . . . 8 Parity relations . . . . . . . . . 94 Inner generators and ordinary differential equations . . 2 ODEs for polynomial inputs f . 4 The global resurgence picture for polynomial inputs f . . . . . .

2 Resurgence of the Gamma function . . . . 3 Monomial/binomial/exponential factors . . . 4 Resummability of the total ingress factor . . 5 Parity relations . . . . . . . . . 4 Inner generators . . . . . . . . . . . 1 Some heuristics . . . . . . . . . 2 The long chain behind nir//mir . . . . . 3 The nir transform . . . . . . . . . 4 The reciprocation transform . . . . . . 5 The mir transform . . . . . . . . 6 Translocation of the nir transform .

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