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Seminarium i matematik

Jesper Göransson: The geometry of second order ordinary differential equations

Välkommen till en föreläsning i seminarieserien i matematik.

Föreläsare/Lecturer

Jesper Göransson, Spyken, Lund

Titel/Title

The geometry of second order ordinary differential equations

Sammanfattning/Abstract

The theory of second order ordinary differential equations has a rich geometric content. A main problem of a second order ODEs is to decide if it can be reduced to the trivial differential equation y''=0. For example are linear equations reducible to the trivial equation.

We will see how this can visualised and understood with the framework of projective geometry, connections, curvature and dual geometry. We will also calculate the instrisic curvature of a general second order ODE and see how this curvature enables us to decide if the differential equation is reducible to the trivial equation.