Publications (6)5.93 Total impact
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ABSTRACT: We show that on any smooth compact connected manifold of dimension $m\geq 2$ admitting a smooth nontrivial circle action $\mathcal{S} = \left\{S_t\right\}_{t \in \mathbb{R}}$, $S_{t+1}=S_t$, the set of weakly mixing $C^{\infty}$diffeomorphisms which preserve both a smooth volume $\nu$ and a measurable Riemannian metric is dense in $\mathcal{A}_{\alpha} \left(M\right)= \overline{ \left\{h \circ S_{\alpha} \circ h^{1} : h \in \text{Diff}^{\infty}\left(M, \nu\right) \right\}}^{C^{\infty}}$ for every Liouvillean number $\alpha$. The proof is based on a quantitative version of the AnosovKatokmethod with explicitly constructed conjugation maps and partitions.  [Show abstract] [Hide abstract]
ABSTRACT: We establish a precise asymptotic formula for the number of homotopy classes of periodic orbits for the geodesic flow on rank one manifolds of nonpositive curvature. This extends a celebrated result of G. A. Margulis to the nonuniformly hyperbolic case and strengthens previous results by G. Knieper. We also establish some useful properties of the measure of maximal entropy.  [Show abstract] [Hide abstract]
ABSTRACT: Some Lyman continuum photons are likely to escape from most galaxies, and these can play an important role in ionizing gas around and between galaxies, including gas that gives rise to Lymanalpha absorption. Thus the gas surrounding galaxies and in the intergalactic medium will be exposed to varying amounts of ionizing radiation depending upon the distances, orientations and luminosities of any nearby galaxies. The ionizing background can be recalculated at any point within a simulation by adding the flux from the galaxies to a uniform quasar contribution. Normal galaxies are found to almost always make some contribution to the ionizing background radiation at a redshift of zero, as seen by absorbers and at random points in space. Assuming that ∼2 per cent of ionizing photons escape from a galaxy such as the Milky Way, we find that normal galaxies make a contribution of at least 30–40 per cent of the assumed quasar background. Lymanalpha absorbers with a wide range of neutral column densities are found to be exposed to a wide range of ionization rates, although the distribution of photoionization rates for absorbers is found to be strongly peaked. On average, fewer highly ionized absorbers are found to arise further from luminous galaxies, while local fluctuations in the ionization rate are seen around galaxies having a wide range of properties.  [Show abstract] [Hide abstract]
ABSTRACT: We show that on a compact manifold of nonpositive curvature the volume of spheres (hence also that of balls) has an exact asymptotic; it is purely exponential, and the growth rate equals the topological entropy. The resulting formula is the sharpest one which is known. It generalizes results of G.A. Margulis to the nonuniformly hyperbolic case. It improves the multiplicative asymptotic bound by G. Knieper.  [Show abstract] [Hide abstract]
ABSTRACT: We describe in detail a construction of weakly mixing C infinity diffeomorphisms preserving a smooth measure and a measurable Riemannian metric as well as Z(k) actions with similar properties. We construct those as a perturbation of elements of a nontrivial nontransitive circle action. Our construction works on all compact manifolds admitting a nontrivial circle action. It is shown in the appendix that a Riemannian metric preserved by a weakly mixing diffeomorphism can not be square integrable.  [Show abstract] [Hide abstract]
ABSTRACT: The full text of the dissertation is available as a Adobe Acrobat .pdf file (94 p.) ; Adobe Acrobat Reader required to view the file. Mode of access: World Wide Web. Thesis (Ph. D.)Pennsylvania State University, 2002.
Publication Stats
16  Citations  
5.93  Total Impact Points  
Top Journals
Institutions

2003

University of Leipzig
 Institute of Mathematics
Leipzig, Saxony, Germany


1999

Pennsylvania State University
 Department of Mathematics
University Park, Maryland, United States
