"Invariants of ordinary differential equations"

Matthias Berth (University Greifswald, Germany).



Abstract: 

We describe the method of Sophus Lie for computing invariants of ODEs
and its implementation using Computer Algebra. Invariants of second
order ODEs have been computed by A. Tresse in a paper from 1896. These
give criteria for determining the type (canonical form) of the symmetry
algebra. For ODEs with free parameters, one can characterize special
cases for which a richer symmetry structure may exist. 
We discuss more specialized settings, i.e. a special class of ODEs 
with a suitably chosen pseudo group of transformations.