Adiabatic invariant of the harmonic oscillator, complex matching and resurgence
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...
| Authors: | , , , |
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| Format: | article |
| Publication Date: | 1997 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/857 |
| Online Access: | https://hdl.handle.net/2117/857 |
| Access Level: | Open access |
| Keyword: | Differential equations 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 |
| Summary: | 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. |
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