Lie systems: theory, generalisations, and applications

J. F. Cariñena, and J. de Lucas. Lie systems: theory, generalisations, and applications. 2011. <http://eudml.org/doc/286020>.

@book{J2011,
abstract = {Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of mapping: the so-called superposition rule. Apart from this fundamental property, Lie systems enjoy many other geometrical features and they appear in multiple branches of mathematics and physics. These facts, together with the authors' recent findings in the theory of Lie systems, led them to write this essay, which aims to describe the new achievements within a self-contained guide to the whole theory of Lie systems, their generalisations, and applications.},
author = {J. F. Cariñena, J. de Lucas},
keywords = {Abel equation; Emden equation; Ermakov system; exact solution; global superposition rule; harmonic oscillator; integrability condition; Lie system; Lie-Scheffers system; Lie-Vessiot system; Lie theorem; Mathews-Lakshmanan oscillator; matrix Riccati equation; Milne-Pinney equation; mixed superposition rule; nonlinear oscillator; partial superposition rule; projective Riccati equation; Riccati equation; Riccati hierarchy; second order Riccati equation; spin Hamiltonian; superposition rule; super-superposition formula},
language = {eng},
title = {Lie systems: theory, generalisations, and applications},
url = {http://eudml.org/doc/286020},
year = {2011},
}

TY - BOOK
AU - J. F. Cariñena
AU - J. de Lucas
TI - Lie systems: theory, generalisations, and applications
PY - 2011
AB - Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of mapping: the so-called superposition rule. Apart from this fundamental property, Lie systems enjoy many other geometrical features and they appear in multiple branches of mathematics and physics. These facts, together with the authors' recent findings in the theory of Lie systems, led them to write this essay, which aims to describe the new achievements within a self-contained guide to the whole theory of Lie systems, their generalisations, and applications.
LA - eng
KW - Abel equation; Emden equation; Ermakov system; exact solution; global superposition rule; harmonic oscillator; integrability condition; Lie system; Lie-Scheffers system; Lie-Vessiot system; Lie theorem; Mathews-Lakshmanan oscillator; matrix Riccati equation; Milne-Pinney equation; mixed superposition rule; nonlinear oscillator; partial superposition rule; projective Riccati equation; Riccati equation; Riccati hierarchy; second order Riccati equation; spin Hamiltonian; superposition rule; super-superposition formula
UR - http://eudml.org/doc/286020
ER -