Loading...
Please wait, while we are loading the content...
Similar Documents
Hamiltonian loops from the ergodic point of view
| Content Provider | Semantic Scholar |
|---|---|
| Author | Polterovich, Leonid |
| Copyright Year | 1999 |
| Abstract | Let G be the group of Hamiltonian diffeomorphisms of a closed symplectic manifold Y . A loop h : S → G is called strictly ergodic if for some irrational number α the associated skew product map T : S × Y → S × Y defined by T (t, y) = (t + α, h(t)y) is strictly ergodic. In the present paper we address the following question. Which elements of the fundamental group of G can be represented by strictly ergodic loops ? We prove existence of contractible strictly ergodic loops for a wide class of symplectic manifolds (for instance for simply connected ones). Further, we find a restriction on the homotopy classes of smooth strictly ergodic loops in the framework of Hofer’s bi-invariant geometry on G. Namely, we prove that their asymptotic Hofer’s norm must vanish. This result provides a link between ergodic theory and symplectic topology. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/9806152v1.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/9806152v2.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Anatomy, Regional Class Ergodic theory Ergodicity Hamiltonian (quantum mechanics) Symplectic integrator Vanish (computer science) manifold |
| Content Type | Text |
| Resource Type | Article |
