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Adiabatic invariant of the harmonic oscillator, complex matching and resurgence
Bonet Revés, Carles; Sauzin, D.; Martínez-Seara Alonso, M. Teresa; València Guitart, Marta
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
The linear oscillator equation with a frequency depending slowly on time is used to test a method to compute exponentially small quantities. This work present the matching method in the complex plane as a tool to obtain rigorously the asymptotic variation of the action of the associated hamiltonian beyond all orders. The solution in the complex plane is aproximated by a series in which all terms present a singularity at the same point. Following matching techniques near this singularity one is led to an equation which does not depend on any parameter, the so-called inner equation, of a Riccati type. This equation is studied by resurgence methods.
Differential equations
Equacions diferencials ordinàries
Equacions diferencials ordinàries
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
Classificació AMS::34 Ordinary differential equations::34A General theory
Classificació AMS::34 Ordinary differential equations::34E Asymptotic theory
Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
Classificació AMS::70 Mechanics of particles and systems::70K Nonlinear dynamics
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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