Linearization of ODEs: Geometric, Complex and Conditional
Starts 10 Aug 2012 12:00
Ends 10 Aug 2012 20:00
Central European Time
Leonardo da Vinci Building Luigi Stasi Seminar Room
Strada Costiera, 11
I - 34151 Trieste (Italy)
In Lie symmetry analysis, linearization is the conversion of a (system of) differential equations to linear form, provided there exists a transformation of the independent and dependent variables that can do so. Lie provided criteria for determining if and when second order scalar ODEs could be so transformed. Considerably later the methods were extended to special classes of third order scalar ODEs. Only recently was there significant progress in this direction. It included the general third and fourth order scalar ODEs and some general results were proved for nth order SCALAR ODEs about the classes of such ODES, and some general results about classes of linearizable second order systems of ODEs. Many more advances have been made more recently by the use of geometry and complex analysis for the purpose. Further, without actually linearizing the system of equations linearization has been used to provide their solution. In this talk these developments will be reviewed.