Computational Methods in Perturbation Theory

Jorba, Àngel

doi:10.1007/978-3-642-27737-5_758-1

Àngel Jorba²

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Glossary

Action-angle variables :: Conjugate set of coordinates for which an integrable Hamiltonian depends only on the actions and, hence, becomes readily integrable.
Canonical transformation :: A canonical transformation is a change of variables that preserve the Hamiltonian form, that is, it is equivalent to perform the change of variables on the Hamiltonian or on the differential equations.
Conformally symplectic systems :: Conformally symplectic systems model dissipative mechanical systems with a friction which is proportional to the velocity. In contrast to conservative systems, dissipative systems have attractors.
Delay differential equation :: A differential equation in which the derivative of the unknown function depends not only of the actual state but also of previous states.
Effective stability :: A system is considered effectively stable if the time needed to observe significant changes is longer than the expected lifetime of the system itself. The study of the effective...

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Acknowledgments

This work has been supported by the Spanish grant PGC2018-100699-B-I00 (MCIU/AEI/FEDER, UE) and the Catalan grant 2017 SGR 1374. The project leading to this application has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 734557.

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Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Barcelona, Spain
Àngel Jorba

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Robert A. Meyers

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Jorba, À. (2022). Computational Methods in Perturbation Theory. In: Meyers, R.A. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_758-1

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DOI: https://doi.org/10.1007/978-3-642-27737-5_758-1
Received: 11 October 2021
Accepted: 10 November 2021
Published: 21 April 2022
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Online ISBN: 978-3-642-27737-5
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