English

Lie families: theory and applications

Classical Analysis and ODEs 2011-11-22 v3 Mathematical Physics Differential Geometry math.MP

Abstract

We analyze families of non-autonomous systems of first-order ordinary differential equations admitting a common time-dependent superposition rule, i.e., a time-dependent map expressing any solution of each of these systems in terms of a generic set of particular solutions of the system and some constants. We next study relations of these families, called Lie families, with the theory of Lie and quasi-Lie systems and apply our theory to provide common time-dependent superposition rules for certain Lie families.

Keywords

Cite

@article{arxiv.1003.3529,
  title  = {Lie families: theory and applications},
  author = {Jose F. Carinena and Janusz Grabowski and Javier de Lucas},
  journal= {arXiv preprint arXiv:1003.3529},
  year   = {2011}
}

Comments

23 pages, revised version to appear in J. Phys. A: Math. Theor

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