Almost every real quadratic map is either regular or stochastic

Every transformation is disjoint from almost every non-classical exchange

A natural generalization of interval exchange maps are linear involutions, first introduced by Danthony and Nogueira. Recurrent train tracks with a single switch which we call non-classical interval exchanges, form a subclass of linear involutions without flips. They are analogs of classical interval exchanges, and are first return maps for non-orientable measured foliations associated to quadratic differentials on Riemann surfaces. We show that every transformation is disjoint from almost every irreducible non-classical interval exchange. In the appendix, we prove that for almost every pair o…

Topology of the regular part for infinitely renormalizable quadratic polynomials

In this paper we describe the well studied process of renormalization of quadratic polynomials from the point of view of their natural extensions. In particular, we describe the topology of the inverse limit of infinitely renormalizable quadratic polynomials and prove that when they satisfy a-priori bounds, the topology is rigid modulo its combinatorics.

Sarnak's Conjecture for Sequences of Almost Quadratic Word Growth

We prove the logarithmic Sarnak conjecture for sequences of subquadratic word growth. In particular, we show that the Liouville function has at least quadratically many sign patterns. We deduce the main theorem from a variant which bounds the correlations between multiplicative functions and sequences with subquadratically many sign patterns which occur with positive logarithmic density. This allows us to actually prove that our multiplicative functions do not locally correlate with sequences of subquadratic word growth. We also prove a conditional result which shows that if the $κ-1$-Fourier …

Among Quadratic Hamiltonians, Bogoliubov Transformations and Non-Regular States on CCRs *-Algebra. I. Pure and Invariant States. (In the Mood for the Manuceau Verbeure Theorems about Quasi-free States and Automorphisma of the CCR Algebra)

The features of the paper are these: 1) we discuss {\bf especially} quadratic (alias bilinear) Bose-Hamiltonians, the related Bogoliubov transformations and {\bf especially} quasi-free-like (alias coherent or Fock-like) states 2) we discuss {\bf any} quadratic Bose-Hamiltonians and Bogoliubov transformations, whether diagonalizable or not, whether proper or improper, and {\bf arbitrary} quasi-free-like states, whether regular or non-regular they are 3) we associate notions and terms of the CCRs theory {CCRs = Canonical Commutation Relations} with notions and terms of the indefinite inner produ…

哪些Meyer集是正则模型集？一种通过殆周期性的刻画

Which Meyer sets are regular model sets? A characterization via almost periodicity

该研究在σ-紧局部紧阿贝尔群的一般框架下，证明了Meyer集是正则模型集的充要条件为其是殆周期图案，完善了Meyer相关结论的逆命题刻画。

关于随机系统中几乎必然可达性的证书

On Certificates for Almost Sure Reachability in Stochastic Systems

本文研究离散时间随机系统的几乎必然可达性证书，证明固定多项式或二次模板会丧失完备性，并刻画加性噪声线性系统中证书存在的矩阵条件。