29 September 2014 to 3 October 2014
International Center for Theoretical Physics
Europe/Paris timezone

Circle actions on the 7-sphere with unbounded periods and non-linearizable multicentres

30 Sep 2014, 11:30
1h
Adriatico Building, Kastler Lecture Hall (International Center for Theoretical Physics)

Adriatico Building, Kastler Lecture Hall

International Center for Theoretical Physics

Strada Costiera, 11 I - 34151 Trieste Italy

Speaker

Massimo VILLARINI (Modena)

Description

We give an example of a free circle action on the 7-dimensional sphere whose orbits have unbounded lenghts (equivalently: unbounded periods).As an application we construct a smooth vector field X in a neighbourhood U of the origin in the 8-dimensional real space such that : U - (0) is foliated by closed integrale curves, the differential DX(0) generate a 1-parametri group of rotations, but X is not orbitally equivalent to its linearization at the origin, hence proving that Poincare' Centre Theorem, true for planar non-degenerate centers is not generalizable in 8 dimensioni.

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