Periodic and constant solutions of matrix Riccati differential equations: n — 2. Proc. Roy. Sur 1’equation differentielle matricielle de type Riccati. Bull. Math. The qualitative study of second order linear equations originated in the classic paper . for a history of the Riccati transformation. Differentielle. (Q(t),’)’. VESSIOT, E.: “Sur quelques equations diffeYentielles ordinaires du second ordre .” Annales de (3) “Sur l’equation differentielle de Riccati du second ordre.

Author: | Bagis Ganris |

Country: | Panama |

Language: | English (Spanish) |

Genre: | Health and Food |

Published (Last): | 16 April 2014 |

Pages: | 68 |

PDF File Size: | 18.52 Mb |

ePub File Size: | 4.74 Mb |

ISBN: | 206-6-52122-867-4 |

Downloads: | 41431 |

Price: | Free* [*Free Regsitration Required] |

Uploader: | Meztihn |

We present a short summary of the Hamiltonian algebrization process that will be used in Section 4.

We never store sensitive information about our customers in cookies. We can see that applying by hand Kovacic Algorithm it can be a lit- tle difficults, but thanks to has been implemented it in Maple command kovacicsols we can avoid such calculations. In this paper a Galoisian approach to build propagators through Riccati equations is presented. Pantazi, On the integrability of polynomial fields in the plane by means of Picard-Vessiot theory, Preprint arXiv: If you have persistent cookies enabled as well, then we will be able to remember you across browser restarts and computer reboots.

Propagators and Green Functions.

Orszag, Quantum OpticsSpringer, Heidelberg, The second author greatly appreciates riccaati support by University of Puerto Rico and Universitat de Barcelona during the academic visit to the latter in Spring where this project was born. Key words and phrases.

## Riccati equation

More generally, the term Riccati equation is used to refer to matrix equations with an analogous quadratic term, which occur in both continuous-time and discrete-time linear-quadratic-Gaussian control.

The correspondence between Riccati equations and second-order linear ODEs has other consequences.

Else, case 1 cannot hold. Gen 18 —30 [15] I.

## Histoire des équations

Beijing, China 51 — [20] C. In this case the ODEs are in the complex domain and differentiation is with respect to a complex variable. Suslov, Models of damped oscillators in quantum mechanics, Journal of Physical Mathematics 1S 16 pages.

Differetielle Hamiltonian 2 had also been considered by Angelow and Trifonov [4, 5] in order to describe the light propagation in a nonlinear anisotropic waveguide.

Suslov, Dynamical invariants for variable quadratic Hamiltonians, Physica Scripta 81 5, 11 pp ; see also Preprint arXiv: The main application of this Ga- loisian approach, for instance a main result of the paper, is the construction of the propagator for the so called degenerate parametric oscillator: Theorem 2 Lie-Kolchin Theorem. The same holds true for the Riccati equation. Log In Sign Up. This page was last edited on 29 Octoberat From Proposition 4, it is recovered the well known result in differential Galois theory see for example [38]: Subscribe to our newsletter Some error text Name.

### Histoire des équations — Wikipédia

Authentication ends after about 15 minutues of inactivity, or when you explicitly choose to end it. Suslov, The Cauchy problem for a forced harmonic oscillatorPreprint arXiv: Kaplansky, An introduction to differential algebra, Hermann, Paris, Ko- vacic in [17] and Hamiltonian Algebrization developed by the first author in [1, 3].

An important eqaution of the Riccati equation is to the 3rd order Schwarzian differential equation. Sometimes, we also use a cookie to keep track of your trolley contents. Ricdati details and proofs can be found in [1, 3].

We consider the differential Galois theory in the context of second order linear differential equations.

### Riccati equation – Wikipedia

For example, at loot. This is the practical aim of this paper, which will be given in Section 4 and in Section 5. The solutions obtained throgh such towers are called Liouvillian.

Remember me on this computer. Views Read Edit View history.