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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...
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...
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...
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...
We add a last refinement to the results of [BW1] and [BW2] re-lating ideal classes of the Weyl algebra to the Calogero-Moser varieties: we show that the bijection constructed in those papers is unique...
The Geometric Cauchy Problem for Surfaces With Lorentzian Harmonic Gauss maps
Differential geometry integrable systems loop groups constant mean curvature surfaces
2010/12/14
The geometric Cauchy problem for a class of surfaces in a pseudo-Riemannian manifold of dimension 3 is to find the surface which contains a given curve with a prescribed tangent bundle along the curve...
Statistical properties of nonuniformly expanding 1d maps with logarithmic singularities
Statistical properties of nonuniformly 1d maps logarithmic singularities
2010/12/13
For a certain parametrized family of maps on the circle, with critical points and
logarithmic singularities where derivatives blow up to infinity, a positive measure set of parameters was constructed...