On Ulam-von Neumann Transformations

On Rigidity of One-Dimensional Maps

The regularity of the conjugacy between two onedimensional maps with singular points is considered. We prove that the conjugacy between two nice and mixing quasi-hyperbolic one-dimensional maps is a diffeomorphism if it is an absolutely continuous homeomorphism and the exponents and the asymmetries of these two maps at all corresponding singular points are the same. We also discuss the applicat...

Asymptotic Hausdorff dimensions of Cantor sets associated with an asymptotically non-hyperbolic family

The geometry of Cantor systems associated with an asymptotically non-hyperbolic family (f )0≤ ≤ 0 was studied by Jiang (Geometry of Cantor systems. Trans. Amer. Math. Soc. 351 (1999), 1975–1987). By applying the geometry studied there, we prove that the Hausdorff dimension of the maximal invariant set of f behaves like 1−K 1/γ asymptotically, as was conjectured by Jiang (Generalized Ulam–von Ne...

Nonlinear $*$-Lie higher derivations on factor von Neumann algebras

Let $mathcal M$ be a factor von Neumann algebra. It is shown that every nonlinear $*$-Lie higher derivation$D={phi_{n}}_{ninmathbb{N}}$ on $mathcal M$ is additive. In particular, if $mathcal M$ is infinite type $I$factor, a concrete characterization of $D$ is given.

Convergence Analysis of Markov Chain Monte Carlo Linear Solvers Using Ulam-von Neumann Algorithm

The convergence of Markov chain–based Monte Carlo linear solvers using the Ulam– von Neumann algorithm for a linear system of the form x = Hx + b is investigated in this paper. We analyze the convergence of the Monte Carlo solver based on the original Ulam–von Neumann algorithm under the conditions that ‖H‖ < 1 as well as ρ(H) < 1, where ρ(H) is the spectral radius of H. We find that although t...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras