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The Torelli group, I(Sg), is the subgroup of the mapping class group consisting of elements that act trivially on the homology of the surface.
Computing the topological entropy of unimodal maps
Topological entropy interval maps symbolic dynamics
2011/3/2
We derive an algorithm to determine recursively the lap number (minimal number of monotone pieces) of the iterates of unimodal maps of an interval with free end-points. The algorithm
is obtained by t...
Exact solution of $D_N$ type quantum Calogero model through a mapping to free harmonic oscillators
Exact solution of $D_N$ type quantum Calogero model mapping to free harmonic oscillators
2010/12/28
We solve the eigenvalue problem of the DN type of Calogero model by mapping it to a set of decoupled quantum harmonic oscillators through a similarity transformation.In particular, we construct the ei...
$L^2$-norm and estimates from below for Riesz transforms on Cantor sets
$L^2$-norm estimates from below Riesz transforms Cantor sets
2011/1/18
The aim of this paper is to estimate the L2-norms of vector-valued Riesz trans-forms Rs
and the norms of Riesz operators on Cantor sets in Rd, as well as to study the distribution of values of Rs ...
It is shown, non–rigorously, that the effective action on Z q– factored odd spheres (lunes) has a vanishing derivative at q = 1. This leaves the effective action on the ordinary sphere as (minus) the ...
On a relation between potentials for pluriharmonic maps and para-pluriharmonic maps
potential pluriharmonic map para-pluriharmonic map the loop group
2011/1/17
In this paper, we show that one can interrelate pluriharmonic maps with para-pluriharmonic maps by means of the loop group method. As an appendix, we give examples for the interrelation between plurih...
Fractional Harmonic Maps into Manifolds in odd dimension n>1
Harmonic maps nonlinear elliptic PDE’s regularity of solutions
2011/1/21
In this paper we consider critical points of the following nonlocal energy Ln(u) = Z IRn |(−)n/4u(x)|2dx , (1) where u: Hn/2(IRn) → N N ⊂ IRm is a compact k dimensional smooth manifold
w...
Lyashko-Looijenga morphisms and submaximal factorisations of a Coxeter element
Lyashko-Looijenga morphisms submaximal factorisations of Coxeter element
2011/2/22
When W is a finite reflection group, the noncrossing partition lattice NCPW of type W is a rich combinatorial object, extending the notion of noncrossing partitions of an n-gon.
We explore Ricci flow coupled with harmonic map flow, both as it arises naturally in certain bundle constructions related to Ricci flow and as a geometric flow in its own right.
Annular area preserving homeomorphisms which admit no interior compact invariant sets
Area preserving homeomorphisms rotation numbers fast approxi-mation by conjugation
2011/2/28
For any irrational number , there exists an ergodic area preserv-ing homeomorphism of the closed annulus which is isotopic to the identitity,admits no compact invariant set contained in the interior ...
The space of toroidal automorphic forms was introduced by Zagier in 1979. Let F be a global field. An automorphic form on GL(2) is toroidal if it has vanishing constant Fourier coefficients along all ...
Hyperbolicity of the invariant sets for the real polynomial maps
Cantor set Complex dynamic Hyperbolic Logistic map Polynomial map
2011/2/25
It is well known that for a > 4, the dynamical behaviors of the logistic map fa(x) = ax(1 − x) on the maximal invariant compact set are “simple”, which could be clearly explained by the theories...
Normal completely positive maps on the space of quantum operations
Completely positive and completely bounded maps Dilation theorems Stinespring representation
2011/2/21
We define a class of higher-order linear maps that transform quantum operations into quantum operations and satisfy suitable requirements of normality and complete positivity. For this class of maps w...
Julia sets of uniformly quasiregular mappings are uniformly perfect
Julia uniformly quasiregular mappings uniformly perfect
2011/1/19
It is well-known that the Julia set J(f) of a rational map f : C → C is uniformly perfect; that is, every ring domain which separates J(f) has bounded modulus,with the bound depending only on f. In th...
Closed-set-based Discovery of Representative Association Rules Revisited
Closed-set-based Discovery Representative Association Rules Revisited
2011/3/2
The output of an association rule miner is often huge in practice.This is why several concise lossless representations have been proposed, such as the “essential” or “representative” rules.