830 research outputs found
There is No Easy Answer: How the Interaction of Content, Situation, and Person Shapes the Effect of Social Media use on Well-being
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 increases as , where is a constant and is the average area occupied by these families. We also find that
increases with 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
Length functions on currents and applications to dynamics and counting
The aim of this (mostly expository) article is twofold. We first explore a
variety of length functions on the space of currents, and we survey recent work
regarding applications of length functions to counting problems. Secondly, we
use length functions to provide a proof of a folklore theorem which states that
pseudo-Anosov homeomorphisms of closed hyperbolic surfaces act on the space of
projective geodesic currents with uniform north-south dynamics.Comment: 35pp, 2 figures, comments welcome! Second version: minor corrections.
To appear as a chapter in the forthcoming book "In the tradition of Thurston"
edited by V. Alberge, K. Ohshika and A. Papadopoulo
Periodic Orbits in Polygonal Billiards
We review some properties of periodic orbit families in polygonal billiards
and discuss in particular a sum rule that they obey. In addition, we provide
algorithms to determine periodic orbit families and present numerical results
that shed new light on the proliferation law and its variation with the genus
of the invariant surface. Finally, we deal with correlations in the length
spectrum and find that long orbits display Poisson fluctuations.Comment: 30 pages (Latex) including 11 figure
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
Automorphisms of graphs of cyclic splittings of free groups
We prove that any isometry of the graph of cyclic splittings of a finitely
generated free group of rank is induced by an outer automorphism
of . The same statement also applies to the graphs of maximally-cyclic
splittings, and of very small splittings.Comment: 22 pages, 5 figures. Small modifications. To appear in Geometriae
Dedicat
Interpopulation Heterogeneity of Deschampsia antarctica Desv According to the Variability of Nuclei Areas and Relative Level of DNA in Different Tissues of Leaves
The objective of the present work was to analyze diversity in several sub-Antarctic populations studying the morphological variability of the average nucleus area in the D. antarctica leaf epidermis and palisade parenchyma and to assess the ability for polysomaty in these tissues. The investigated material gathered on 5 islands of sub-Antarctica: Petermann, Berthelot, Galindez, Rasmussen and Yalour, thus the populations experienced quit different conditions.Целью этого исследования было изучение наличия полисоматии в тканях листа D. antarctica, а также анализ межпопуляционной изменчивости по величине средней площади ядра и относительного содержания ДНК в ядрах клеток эпидермальной и паренхимной тканей листка D. antarctica. В исследовании использовали материал, собранный в марте 2005 г. на пяти островах Субантарктики: Петерман, Бертелот, Галиндез, Расмуссен и Ялур.Метою цього дослідження було вивчити наявність полісоматії в тканинах листка D. antarctica, а також проаналізувати міжпопуляційну мінливість за величиною середньої площі ядра та відносного вмісту ДНК в ядрі клітин епідермальної та паренхімної тканин листка цієї рослини. В дослідженні використовували матеріал, зібраний в березні 2005 р. на п’ятьох островах Субантарктики: Петерман, Бертелот, Галіндез, Расмуссен та Ялу
Square-tiled cyclic covers
A cyclic cover of the complex projective line branched at four appropriate
points has a natural structure of a square-tiled surface. We describe the
combinatorics of such a square-tiled surface, the geometry of the corresponding
Teichm\"uller curve, and compute the Lyapunov exponents of the determinant
bundle over the Teichm\"uller curve with respect to the geodesic flow. This
paper includes a new example (announced by G. Forni and C. Matheus in
\cite{Forni:Matheus}) of a Teichm\"uller curve of a square-tiled cyclic cover
in a stratum of Abelian differentials in genus four with a maximally degenerate
Kontsevich--Zorich spectrum (the only known example found previously by Forni
in genus three also corresponds to a square-tiled cyclic cover
\cite{ForniSurvey}).
We present several new examples of Teichm\"uller curves in strata of
holomorphic and meromorphic quadratic differentials with maximally degenerate
Kontsevich--Zorich spectrum. Presumably, these examples cover all possible
Teichm\"uller curves with maximally degenerate spectrum. We prove that this is
indeed the case within the class of square-tiled cyclic covers.Comment: 34 pages, 6 figures. Final version incorporating referees comments.
In particular, a gap in the previous version was corrected. This file uses
the journal's class file (jmd.cls), so that it is very similar to published
versio
Generic Continuous Spectrum for Ergodic Schr"odinger Operators
We consider discrete Schr"odinger operators on the line with potentials
generated by a minimal homeomorphism on a compact metric space and a continuous
sampling function. We introduce the concepts of topological and metric
repetition property. Assuming that the underlying dynamical system satisfies
one of these repetition properties, we show using Gordon's Lemma that for a
generic continuous sampling function, the associated Schr"odinger operators
have no eigenvalues in a topological or metric sense, respectively. We present
a number of applications, particularly to shifts and skew-shifts on the torus.Comment: 14 page
Quadratic differentials as stability conditions
We prove that moduli spaces of meromorphic quadratic differentials with
simple zeroes on compact Riemann surfaces can be identified with spaces of
stability conditions on a class of CY3 triangulated categories defined using
quivers with potential associated to triangulated surfaces. We relate the
finite-length trajectories of such quadratic differentials to the stable
objects of the corresponding stability condition.Comment: 123 pages; 38 figures. Version 2: hypotheses in the main results
mildly weakened, to reflect improved results of Labardini-Fragoso and
coauthors. Version 3: minor changes to incorporate referees' suggestions.
This version to appear in Publ. Math. de l'IHE
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