A geometric approach to integrability conditions for Riccati equations.
A super-integrable two-dimensional nonlinear oscillator with an exactly solvable quantum analog.
Recent applications of the theory of Lie systems in Ermakov systems.
Emmy Noether: innovación y creatividad en Ciencia.
Applications of Lie systems in quantum mechanics and control theory
Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum problems can be treated in a similar way, may be up to the replacement of the Lie group involved by a central extension of it. The geometric techniques developed for dealing with Lie systems are also used in problems of control theory. Specifically, we will study...
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