## Dynamical Systems

•  Huyi Hu, MSU
•  The essential coexistence phenomenon in Hamiltonian dynamics
•  03/26/2019
•  3:00 PM - 4:00 PM
•  C117 Wells Hall

We construct an example of a Hamiltonian flow $f^t$ on a $4$-dimensional smooth manifold $\mathcal{M}$ which after being restricted to an energy surface $\mathcal{M}_e$ demonstrates essential coexistence of regular and chaotic dynamics, that is, there is an open and dense $f^t$-invariant subset $U\subset\mathcal{M}_e$ such that the restriction $f^t|U$ has non-zero Lyapunov exponents in all directions (except the direction of the flow) and is a Bernoulli flow while on the boundary $\partial U$, which has positive volume, all Lyapunov exponents of the system are zero. This is a continuation of the talk given in previous weeks.

## Contact

Department of Mathematics
Michigan State University