An estimate for the entropy of Hamiltonian flows
| dc.contributor.area | Mathematics | en_US |
| dc.contributor.author | Chittaro, Francesca C. | en_US |
| dc.contributor.department | Functional Analysis and Applications | en_US |
| dc.date.accessioned | 2006-04-18T12:42:32Z | en_US |
| dc.date.accessioned | 2011-09-07T20:27:40Z | |
| dc.date.available | 2006-04-18T12:42:32Z | en_US |
| dc.date.available | 2011-09-07T20:27:40Z | |
| dc.date.issued | 2006-04-18T12:42:32Z | en_US |
| dc.description.abstract | In the paper we present a generalization to Hamiltonian flows on symplectic manifolds of the estimate proved by Ballmann and Wojtkovski in \cite{BaWoEnGeo} for the dynamical entropy of the geodesic flow on a compact Riemannian manifold of nonpositive sectional curvature. Given such a Riemannian manifold $M,$ Ballmann and Wojtkovski proved that the dynamical entropy $h_{\mu}$ of the geodesic flow on $M$ satisfies the following inequality: $$ h_{\mu} \geq \int_{SM} \traccia \sqrt{-K(v)} d\mu(v), $$ \noindent where $v$ is a unit vector in $T_pM$, if $p$ is a point in $M$, $SM$ is the unit tangent bundle on $M,$ $K(v)$ is defined as $K(v) = \mathcal{R}(\cdot,v)v$, with $\mathcal{R}$ Riemannian curvature of $M$, and $\mu$ is the normalized Liouville measure on $SM$. | en_US |
| dc.format.extent | 169771 bytes | en_US |
| dc.format.mimetype | application/pdf | en_US |
| dc.identifier.citation | J. Dyn. Control Syst. 13 (2007) 55-67 | en_US |
| dc.identifier.uri | https://openscience.sissa.it/handle/1963/1815 | en_US |
| dc.language.iso | en_US | en_US |
| dc.relation.ispartofseries | SISSA;09/2006/M | en_US |
| dc.relation.ispartofseries | arXiv.org;math.DS/0602674 | en_US |
| dc.relation.uri | 10.1007/s10883-006-9003-3 | en_US |
| dc.title | An estimate for the entropy of Hamiltonian flows | en_US |
| dc.type | Preprint | en_US |