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# An estimate for the entropy of Hamiltonian flows

 dc.contributor.author Chittaro, Francesca C. 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.identifier.citation J. Dyn. Control Syst. 13 (2007) 55-67 en_US dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/1815 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.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 dc.contributor.department Functional Analysis and Applications en_US dc.contributor.area Mathematics en_US
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