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Título
A Review in Ermakov Systems and Their Symmetries
Autor(es)
Materia
Ermakov system
Symmetry of dynamical system
Integrability
Clasificación UNESCO
1202 Análisis y Análisis Funcional
Fecha de publicación
2021-03-17
Editor
MDPI
Citación
Cerveró, J.M.; Estévez, P.G. A Review in Ermakov Systems and Their Symmetries. Symmetry 2021, 13, 493. https://doi.org/10.3390/sym13 030493
Resumen
[EN]A review of the mathematical and physical aspects of the Ermakov systems is presented. The main properties of Lie algebra invariants are extensively used. The two and tridimensional Ermakov systems are fully analyzed and the correspondent invariants found. Then, we go over quantization with special emphasis in the two dimensional case. An application to Nonlinear Optics is hereby developed. We also treat the so-called “one dimensional” case, which is easily solved in the classical case but offers special interest in the quantum realm, where one can find exactly the Feynman propagator. We finish with the stationary phase approximation which contains also some interesting features when compared with the exact solution. Some prospects for future research are also discussed.
URI
ISSN
2073-8994
DOI
10.3390/sym13030493
Versión del editor
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