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This article concerns the locus of all locally constant $\mathrm{SL}(2,\mathbb{R})$-valued cocycles that are uniformly hyperbolic, called the hyperbolic locus. Using the theory of semigroups of M\"obius transformations we introduce a new…

It follows from Oseledec Multiplicative Ergodic Theorem that the Lyapunov-irregular set of points for which the Oseledec averages of a given continuous cocycle diverge has zero measure with respect to any invariant probability measure. In…

This paper discusses the stabilizability, weak stabilizability, exact observability and robust quadratic stabilizability of linear stochastic control systems. By means of the spectrum technique of the generalized Lyapunov operator, a…

In this paper we presents new deterministic approximations to the least square mean, also called geometric mean or barycenter of a finite collection of positive definite matrices. Let A1, A2, ..., Am be any elements of Md(C)+, where the set…

Following V. I. Arnold, we define the stochasticity parameter $S(U)$ of a subset $U$ of $\mathbb{Z}/M\mathbb{Z}$ to be the sum of squares of the consecutive distances between elements of $U$. In this paper we study the stochasticity…

We analyze the performance of a variant of Newton method with quadratic regularization for solving composite convex minimization problems. At each step of our method, we choose regularization parameter proportional to a certain power of the…

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional)…

It is known (see \cite[Br\"and\'en, Lemma 2.7]{B10}) that a necessary condition for $T:=\sum Q_k(x) D^k$ to be hyperbolicity preserving is that $Q_k(x)$ and $Q_{k-1}(x)$ have interlacing zeros. We characterize all quadratic linear…

In this paper we consider generalized eigenvalue problems for a family of operators with a quadratic dependence on a complex parameter. Our model is $L(\lambda)=-\triangle +(P(x)-\lambda)^2$ in $L^2(\R^d)$ where $P$ is a positive elliptic…

In this paper, we introduce a new generalization of Pascal's triangle. The new object is called the hyperbolic Pascal triangle since the mathematical background goes back to regular mosaics on the hyperbolic plane. We describe precisely the…

A cubic polynomial $P$ with a non-repelling fixed point $b$ is said to be immediately renormalizable if there exists a (connected) QL invariant filled Julia set $K^*$ such that $b\in K^*$. In that case, exactly one critical point of $P$…

The Chromomagnetic operator (CMO) mixes with a large number of operators under renormalization. We identify which operators can mix with the CMO, at the quantum level. Even in dimensional regularization (DR), which has the simplest mixing…

We consider scalar-input control systems in the vicinity of an equilibrium, at which the linearized systems are not controllable. For finite dimensional control systems, the authors recently classified the possible quadratic behaviors.…

We give sufficient conditions for a parametrised family of probability measures on a Riemannian manifold with boundary to be represented by random maps of class $C^k$. The conditions allow for the probability densities to approach zero…

This work introduces a new cubic regularization method for nonconvex unconstrained multiobjective optimization problems. At each iteration of the method, a model associated with the cubic regularization of each component of the objective…

We consider C^2 families t->f_t of C^4 nondegenerate unimodal maps. We study the absolutely continuous invariant probability (SRB) measure m_t of f_t, as a function of t on the set of Collet-Eckmann (CE) parameters: Upper bounds: Assuming…

We examine the linear convergence rates of variants of the proximal point method for finding zeros of maximal monotone operators. We begin by showing how metric subregularity is sufficient for linear convergence to a zero of a maximal…

We study the dynamics of a family of replicator maps, depending on two parameters. Such studies are motivated by the analysis of the dynamics of evolutionary games under selections. From the dynamics viewpoint, we prove the existence of…

We consider a complete, unbounded, hyperbolic metric space $X$ and a concave, nonzero and nondecreasing function $\omega:[0,+\infty)\to[0,+\infty)$ with $\omega(0)=0$ and study the space $\mathcal{C}_\omega(X)$ of uniformly continous…

We consider a class of cubic stochastic operators that are motivated by models for evolution of frequencies of genetic types in populations. We take populations with three mutually exclusive genetic types. The long term dynamics of single…