On Cr−C^r-closing for flows on 2-manifolds

For some full measure subset B of the set of iet's (i.e. interval exchange transformations) the following is satisfied: Let X be a $C^r$, $1\le r\le \infty$, vector field, with finitely many singularities, on a compact orientable surface M. Given a nontrivial recurrent point $p\in M$ of X, the holonomy map around p is semi-conjugate to an iet $E :[0,1) \to [0,1).$ If $E\in B$ then there exists a $C^r$ vector field Y, arbitrarily close to X, in the $C^r-$topology, such that Y has a closed trajectory passing through p.Comment: 7 pages, 1 figur

Ergodic directions for billiards in a strip with periodically located obstacles

We study the size of the set of ergodic directions for the directional billiard flows on the infinite band $\R\times [0,h]$ with periodically placed linear barriers of length $0<\lambda<h$. We prove that the set of ergodic directions is always uncountable. Moreover, if $\lambda/h\in(0,1)$ is rational the Hausdorff dimension of the set of ergodic directions is greater than 1/2. In both cases (rational and irrational) we construct explicitly some sets of ergodic directions.Comment: The article is complementary to arXiv:1109.458

Vaginal hormone-free moisturising cream is not inferior to an estriol cream for treating symptoms of vulvovaginal atrophy: Prospective, randomised study.

This prospective, open-label, multicentre, multinational, randomised trial investigated the non-inferiority of treatment with a vaginal hormone-free moisturising cream compared to a vaginal estriol (0.1%) cream in a panel of post-menopausal women suffering from symptoms of vulvovaginal dryness in a parallel group design. In total, 172 post-menopausal women were randomly allocated to either one of the two treatments, each administered for 43 days. The primary endpoint was the total severity score of subjective symptoms (dryness, itching, burning and pain unrelated to sexual intercourse) of the respective treatment period. Secondary endpoints were severity of single subjective symptoms (including dyspareunia if sexually active), impairment of daily life, Vaginal Health Index, as well as assessment of safety. In both groups, women treated with hormone-free moisturising cream and those treated with estriol cream, total severity score improved significantly compared to baseline by 5.0 (from 6.1 to 1.1) and by 5.4 (from 6.0 to 0.6), respectively, after 43 days of treatment (p < 0.0001). One-sided test of baseline differences (for a clinically relevant difference Δ = 1.5) confirmed the hormone-free moisturising cream to be non-inferior to the estriol cream. Severity of dyspareunia as well as impairment of daily life due to subjective symptoms, significantly improved for both treatment groups (p<0.0001). Subgroup analysis of women with mild or moderate impairment of daily life at baseline caused by "vaginal dryness" symptoms benefited from both creams, while women with severe impairment showed a significantly greater benefit from the estriol cream (p = 0.0032). Both treatments were well tolerated with no serious adverse events occurring. This study provides clinical evidence that a hormone-free vaginal moisturising cream cannot only improve vaginal dryness compared to an 0.1% estriol cream but also can relieve dyspareunia as well as improve woman's impairment of daily life, justifying its use as a first choice for mild or moderate vulvovaginal dryness symptoms

Comment on "c-axis Josephson tunneling in Dx2−y2D_{x^2-y^2}-wave superconductors''

This comment points out that the recent paper by Maki and Haas [Phys. Rev. B {\bf 67}, 020510 (2003)] is completely wrong.Comment: 1 page, submittted to Phys. Rev.

Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow

We compute the sum of the positive Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow. The computation is based on the analytic Riemann-Roch Theorem and uses a comparison of determinants of flat and hyperbolic Laplacians when the underlying Riemann surface degenerates.Comment: Minor corrections. To appear in Publications mathematiques de l'IHE

Periodic Orbits and Spectral Statistics of Pseudointegrable Billiards

We demonstrate for a generic pseudointegrable billiard that the number of periodic orbit families with length less than $l$ increases as $\pi b_0l^2/\langle a(l) \rangle$, where $b_0$ is a constant and $\langle a(l) \rangle$ is the average area occupied by these families. We also find that $\langle a(l) \rangle$ increases with $l$ before saturating. Finally, we show that periodic orbits provide a good estimate of spectral correlations in the corresponding quantum spectrum and thus conclude that diffraction effects are not as significant in such studies.Comment: 13 pages in RevTex including 5 figure

Thurston's pullback map on the augmented Teichm\"uller space and applications

Let $f$ be a postcritically finite branched self-cover of a 2-dimensional topological sphere. Such a map induces an analytic self-map $\sigma_f$ of a finite-dimensional Teichm\"uller space. We prove that this map extends continuously to the augmented Teichm\"uller space and give an explicit construction for this extension. This allows us to characterize the dynamics of Thurston's pullback map near invariant strata of the boundary of the augmented Teichm\"uller space. The resulting classification of invariant boundary strata is used to prove a conjecture by Pilgrim and to infer further properties of Thurston's pullback map. Our approach also yields new proofs of Thurston's theorem and Pilgrim's Canonical Obstruction theorem.Comment: revised version, 28 page