Bowen entropy for actions of amenable groups

Bowen introduced a definition of topological entropy of subset inspired by Hausdorff dimension in 1973 \cite{B}. In this paper we consider the Bowen's entropy for amenable group action dynamical systems and show that under the tempered condition, the Bowen entropy of the whole compact space for a given F{\o}lner sequence equals to the topological entropy. For the proof of this result, we establish a variational principle related to the Bowen entropy and the Brin-Katok's local entropy formula for dynamical systems with amenable group actions.Comment: 13 page

Performance of the Bowen ratio systems on a 22 deg slope

The Bowen ratio energy balance technique was used to assess the energy fluxes on inclined surfaces during the First ISLSCP Field Experiment (FIFE). Since air flow over sloping surface may differ from that over flat terrain, it is important to examine whether Bowen ratio measurements taken on sloping surfaces are valid. In this study, the suitability of using the Bowen ratio technique on sloping surfaces was tested by examining the assumptions that the technique requires for valid measurements. This was accomplished by studying the variation of Bowen ratio measurements along a selected slope at the FIFE site. In September 1988, four Bowen ratio systems were set up in a line along the 22 degree north-facing slope with northerly air flow (wind went up the slope). In July of 1989, six Bowen ratio systems were similarly installed with southerly air flow (the wind went down slope). Results indicated that, at distances between 10 to 40 meters from the top of the slope, no temperature or vapor pressure gradient parallel to the slope was detected. Uniform Bowen ratio values were obtained on the slope, and thus the sensible or latent heat flux should be similar along the slope. This indicates that the assumptions for valid flux measurements are reasonably met at the slope. The Bowen ratio technique should give the best estimates of the energy fluxes on slopes similar to that in this study

Evolving the Bowen-York initial data for spinning black holes

The Bowen-York initial value data typically used in numerical relativity to represent spinning black hole are not those of a constant-time slice of the Kerr spacetime. If Bowen-York initial data are used for each black hole in a collision, the emitted radiation will be partially due to the ``relaxation'' of the individual holes to Kerr form. We compute this radiation by treating the geometry for a single hole as a perturbation of a Schwarzschild black hole, and by using second order perturbation theory. We discuss the extent to which Bowen-York data can be expected accurately to represent Kerr holes.Comment: 10 pages, RevTeX, 4 figures included with psfi

Follow Me: Building an Online Brand

Kellie Bowen ’18 scrolls methodically through Facebook on a recent afternoon, Judas Priest screaming through her ear buds. The British band hooked her on heavy metal at age 10, the first time she heard the insistent thump of the bass, howl of the electric guitar and operatic singing of front man Rob Halford. What do you do when you have a deep passion, like Bowen developed for metal? For Bowen, and others in today’s always-on, instantly connected digital world, the choice seemed obvious – create an online platform, connect with like-minded metalheads and motivate others along the way

Flat strips, Bowen-Margulis measures, and mixing of the geodesic flow for rank one CAT(0) spaces

Let $X$ be a proper, geodesically complete CAT(0) space under a proper, non-elementary, isometric action by a group $\Gamma$ with a rank one element. We construct a generalized Bowen-Margulis measure on the space of unit-speed parametrized geodesics of $X$ modulo the $\Gamma$-action. Although the construction of Bowen-Margulis measures for rank one nonpositively curved manifolds and for CAT(-1) spaces is well-known, the construction for CAT(0) spaces hinges on establishing a new structural result of independent interest: Almost no geodesic, under the Bowen-Margulis measure, bounds a flat strip of any positive width. We also show that almost every point in $\partial_\infty X$, under the Patterson-Sullivan measure, is isolated in the Tits metric. (For these results we assume the Bowen-Margulis measure is finite, as it is in the cocompact case). Finally, we precisely characterize mixing when $X$ has full limit set: A finite Bowen-Margulis measure is not mixing under the geodesic flow precisely when $X$ is a tree with all edge lengths in $c \mathbb Z$ for some $c > 0$. This characterization is new, even in the setting of CAT(-1) spaces. More general (technical) versions of these results are also stated in the paper.Comment: v2: 26 pages, 1 figure. Theorems stated in much more generality (in particular, the cocompactness hypothesis was removed almost everywhere), also a number of proofs dropped. This is the July 2015 version that was accepted for publication in Ergodic Theory and Dynamical Systems. v1: 39 pages, 1 figur

Bowen-York Tensors

There is derived, for a conformally flat three-space, a family of linear second-order partial differential operators which send vectors into tracefree, symmetric two-tensors. These maps, which are parametrized by conformal Killing vectors on the three-space, are such that the divergence of the resulting tensor field depends only on the divergence of the original vector field. In particular these maps send source-free electric fields into TT-tensors. Moreover, if the original vector field is the Coulomb field on $\mathbb{R}^3\backslash \lbrace0\rbrace$, the resulting tensor fields on $\mathbb{R}^3\backslash \lbrace0\rbrace$ are nothing but the family of TT-tensors originally written down by Bowen and York.Comment: 12 pages, Contribution to CQG Special Issue "A Spacetime Safari: Essays in Honour of Vincent Moncrief