### On Herman positive metric entropy conjecture

- Series
- CDSNS Colloquium
- Time
- Friday, March 11, 2022 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Online via Zoom
- Speaker
- Dmitry Turaev – Imperial College – d.turaev@imperial.ac.uk

**Please Note:** Link: https://us06web.zoom.us/j/83392531099?pwd=UHh2MDFMcGErbzFtMHBZTmNZQXM0dz09

Consider any area-preserving map of R2 which has an elliptic periodic orbit. We show that arbitrarily close to this map (in the C-infinity topology) there exists an area-preserving map which has a "chaotic island" - an open set where every point has positive maximal Lyapunov exponent. The result implies that the naturally sound conjectures that relate the observed chaotic behavior in non-hyperbolic conservative systems with the positivity of the metric entropy need a rethinking.