### Lie transform

**(Lie transformation)**
(type of infinitesimal transform)

A **Lie transform** or **Lie transformation** is
a specific type of **infinitesimal transform/transformation**
(arbitrarily small transformations) of **manifolds** that
form a type of **transformation group** termed a **Lie group**,
which has an associated algebra (**Lie algebra**).
They can be used in the development of perturbation theories,
using **abstract algebra** concepts and methods
to handle the differential equations of
Hamiltonian mechanical systems.
This is used for analysis of orbits in
celestial mechanics as well as in
electron orbits.
*Lie transforms*, *Lie groups* and *Lie algebras*
are based on underlying work by the mathematician Sophus Lie
and named for him.

(*mathematics,differential equations,celestial mechanics,orbits*)
**Further reading:**

http://en.wikipedia.org/wiki/Infinitesimal_transformation

http://en.wikipedia.org/wiki/Lie_group

http://en.wikipedia.org/wiki/Lie_algebra

http://en.wikipedia.org/wiki/Lie_theory

https://pages.uoregon.edu/arkadiy/howe.very.basic.lie.theory.pdf

https://arxiv.org/abs/1104.1106

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