Fiberwise volume growth via Lagrangian intersections
| dc.creator | Frauenfelder, Urs | |
| dc.creator | Schlenk, Felix | |
| dc.date | 2005-04-06 | |
| dc.date.accessioned | 2026-07-07T05:18:50Z | |
| dc.date.available | 2026-07-07T05:18:50Z | |
| dc.description | We consider Hamiltonian diffeomorphisms $ϕ$ of the unit cotangent bundle over a closed Riemannian manifold $(M,g)$ which extend to Hamiltonian diffeomorphisms of $T^*M$ equal to the time-1-map of the geodesic flow for $|p| \ge 1$. For such diffeomorphisms we establish uniform lower bounds for the fiberwise volume growth of $ϕ$ which were previously known for geodesic flows and which depend only on $(M,g)$ or on the homotopy type of $M$. More precisely, we show that for each $q \in M$ the volume growth of the unit ball in $T_q^*M$ under the iterates of $ϕ$ is at least linear if $M$ is rationally elliptic, is exponential if $M$ is rationally hyperbolic, and is bounded from below by the growth of the fundamental group of $M$. In the case that all geodesics of $g$ are closed, we conclude that the slow volume growth of every symplectomorphism in the symplectic isotopy class of the Dehn--Seidel twist is at least 1, completing the main result of \cite{FS:GAFA}. The proofs use the Lagrangian Floer homology of $T^*M$ and the Abbondandolo--Schwarz isomorphism from this homology to the homology of the based loop space of $M$. | |
| dc.description | 19 pages, latex2e | |
| dc.identifier | https://arxiv.org/abs/math/0504099 | |
| dc.identifier | http://arxiv.org/abs/math/0504099 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74805 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Dynamical Systems | |
| dc.subject | 53D35 | |
| dc.title | Fiberwise volume growth via Lagrangian intersections | |
| dc.type | text |