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EXPONENTIAL THURSTON MAPS AND LIMITS OF QUADRATIC DIFFERENTIALS
Quadratic differential decomposition limit model iteration exponential map classification
2015/8/26
In the theory of iterated rational maps, the easiest maps to understand are postcritically finite: maps whose critical orbits are all periodic or preperiodic. These maps are also the most important ma...
Word maps with small image in simple groups
Word maps with small image simple groups Group Theory
2012/6/25
We construct non-power words which have small image in SL(2; 22n) for each n. In particular, the corresponding word maps are non-surjective. We also use this to construct word maps whose values are pr...
Cannon-Thurston maps do not always exist
hyperbolic group Cannon–Thurston map Group Theory
2012/6/19
We construct an example of a hyperbolic group with a hyperbolic subgroup for which the Cannon-Thurston map does not exist. That is, inclusion does not induce a map of the boundaries.
Assembly maps with coefficients in topological algebras and the integral K-theoretic Novikov conjecture
topological algebras the integral K-theoretic Novikov conjecture K-Theory and Homology Algebraic Topology
2011/9/2
Abstract: We prove that any countable discrete and torsion free subgroup of a general linear group over an arbitrary field or a similar subgroup of an almost connected Lie group satisfies the integral...
Three commuting, unital, completely positive maps that have no minimal dilation
Product system subproduct system semigroups of completely positive maps
2011/1/20
In this note we prove that there exist at least two examples of three commuting, unital, completely positive maps that have no dilation on a type I factor, and no minimal dilation on any von Neumann a...
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...
Homogeneous spaces, multi-moment maps and (2,3)-trivial algebras
Homogeneous spaces multi-moment maps (2,3)-trivial algebras
2011/1/17
For geometries with a closed three-form we briefly overview the notion of multimoment maps. We then give concrete examples of multi-moment maps for homogeneous hypercomplex and nearly K¨ahler manifold...
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...
On the derivation algebra of the free Lie algebra and trace maps
derivation algebra free Lie algebra trace maps
2011/1/20
In this paper, we mainly study the derivation algebra of the free Lie algebra and the Chen Lie algebra generated by the abelianization H of a free group, and trace maps.
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...
Extension results for boolean maps and a class of systems of linear inequalities
Involution posets boolean maps systems of linear inequalities
2011/2/28
In this paper we introduce the notion of core for two specific classes of boolean maps on finite involution posets (which are a generalization of the boolean lattices) and we prove some extension resu...
Dynamics of continued fractions and kneading sequences of unimodal maps
Dynamics of continued fractions kneading sequences of unimodal maps
2011/1/20
The goal of this paper is to provide a link between the parameter spaces of two families of one-dimensional dynamical systems, and to shed some light onto some sets of numbers which arise as “exceptio...