The generic symplectic \(C^1\)-diffeomorphisms of four-dimensional symplectic manifolds are hyperbolic, partially hyperbolic or have a completely elliptic periodic point. (English) Zbl 1030.37037
The title of this paper reflects well the main result. More precisely, a refinement of a result of S. E. Newhouse [Am. J. Math. 99, 1061-1087 (1977; Zbl 0379.58011)] is given in a four-dimensional case.
Reviewer: Jan Andres (Olomouc)
MSC:
| 37J10 | Symplectic mappings, fixed points (dynamical systems) (MSC2010) |
| 37C05 | Dynamical systems involving smooth mappings and diffeomorphisms |
| 37C20 | Generic properties, structural stability of dynamical systems |
| 37D20 | Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) |
| 37D30 | Partially hyperbolic systems and dominated splittings |
| 37C25 | Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics |
