75 research outputs found
On second order elliptic equations with a small parameter
The Neumann problem with a small parameter
is
considered in this paper. The operators and are self-adjoint second
order operators. We assume that has a non-negative characteristic form
and is strictly elliptic. The reflection is with respect to inward
co-normal unit vector . The behavior of
is effectively described via
the solution of an ordinary differential equation on a tree. We calculate the
differential operators inside the edges of this tree and the gluing condition
at the root. Our approach is based on an analysis of the corresponding
diffusion processes.Comment: 28 pages, 1 figure, revised versio
Geometric representation of interval exchange maps over algebraic number fields
We consider the restriction of interval exchange transformations to algebraic
number fields, which leads to maps on lattices. We characterize
renormalizability arithmetically, and study its relationships with a
geometrical quantity that we call the drift vector. We exhibit some examples of
renormalizable interval exchange maps with zero and non-zero drift vector, and
carry out some investigations of their properties. In particular, we look for
evidence of the finite decomposition property: each lattice is the union of
finitely many orbits.Comment: 34 pages, 8 postscript figure
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
The Right Place at the Right Time: Creative Spaces in Libraries
Purpose
This essay explores the recent trend in libraries: that of the establishment of spaces specifically set aside for creative work. The rise of these dedicated creative spaces is owed to a confluence of factors that happen to be finding their expression together in recent years. This essay examines the history of these spaces and explores the factors that gave rise to them and will fuel them moving forward.
Design/Methodology/Approach
A viewpoint piece, this essay combines historical research and historical/comparative analyses to examine the ways by which libraries have supported creative work in the past and how they may continue to do so into the 21st century.
Findings
The key threads brought together include a societal recognition of the value of creativity and related skills and attributes; the philosophies, values, and missions of libraries in both their longstanding forms and in recent evolutions; the rise of participatory culture as a result of inexpensive technologies; improved means to build community and share results of efforts; and library experience and historical practice in matters related to creativity. The chapter concludes with advice for those interested in the establishment of such spaces, grounding those reflections in the author’s experiences in developing a new creative space at Virginia Commonwealth University.
Originality/value
While a number of pieces have been written that discuss the practicalities of developing certain kinds of creative spaces, very little has been written that situates these spaces in larger social and library professional contexts; this essay begins to fill that gap
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
Quasiperiodic functions theory and the superlattice potentials for a two-dimensional electron gas
We consider Novikov problem of the classification of level curves of
quasiperiodic functions on the plane and its connection with the conductivity
of two-dimensional electron gas in the presence of both orthogonal magnetic
field and the superlattice potentials of special type. We show that the
modulation techniques used in the recent papers on the 2D heterostructures
permit to obtain the general quasiperiodic potentials for 2D electron gas and
consider the asymptotic limit of conductivity when . Using the
theory of quasiperiodic functions we introduce here the topological
characteristics of such potentials observable in the conductivity. The
corresponding characteristics are the direct analog of the "topological
numbers" introduced previously in the conductivity of normal metals.Comment: Revtex, 16 pages, 12 figure
Amoebas of complex hypersurfaces in statistical thermodynamics
The amoeba of a complex hypersurface is its image under a logarithmic
projection. A number of properties of algebraic hypersurface amoebas are
carried over to the case of transcendental hypersurfaces. We demonstrate the
potential that amoebas can bring into statistical physics by considering the
problem of energy distribution in a quantum thermodynamic ensemble. The
spectrum of the ensemble is assumed to be
multidimensional; this leads us to the notions of a multidimensional
temperature and a vector of differential thermodynamic forms. Strictly
speaking, in the paper we develop the multidimensional Darwin and Fowler method
and give the description of the domain of admissible average values of energy
for which the thermodynamic limit exists.Comment: 18 pages, 5 figure
Normal families of functions and groups of pseudoconformal diffeomorphisms of quaternion and octonion variables
This paper is devoted to the specific class of pseudoconformal mappings of
quaternion and octonion variables. Normal families of functions are defined and
investigated. Four criteria of a family being normal are proven. Then groups of
pseudoconformal diffeomorphisms of quaternion and octonion manifolds are
investigated. It is proven, that they are finite dimensional Lie groups for
compact manifolds. Their examples are given. Many charactersitic features are
found in comparison with commutative geometry over or .Comment: 55 pages, 53 reference
Limit theorems for self-similar tilings
We study deviation of ergodic averages for dynamical systems given by
self-similar tilings on the plane and in higher dimensions. The main object of
our paper is a special family of finitely-additive measures for our systems. An
asymptotic formula is given for ergodic integrals in terms of these
finitely-additive measures, and, as a corollary, limit theorems are obtained
for dynamical systems given by self-similar tilings.Comment: 36 pages; some corrections and improved exposition, especially in
Section 4; references adde
Ergodic infinite group extensions of geodesic flows on translation surfaces
We show that generic infinite group extensions of geodesic flows on square
tiled translation surfaces are ergodic in almost every direction, subject to
certain natural constraints. Recently K. Fr\c{a}czek and C. Ulcigrai have shown
that certain concrete staircases, covers of square-tiled surfaces, are not
ergodic in almost every direction. In contrast we show the almost sure
ergodicity of other concrete staircases. An appendix provides a combinatorial
approach for the study of square-tiled surfaces
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