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This paper concerns the recently proposed quasi-balanced truncation model reduction method for linear quantum stochastic systems. It has previously been shown that the quasi-balanceable class of systems (i.e. systems that can be truncated…

Motivated by the concept of Quasi-Sliding Mode (QSM) in discrete-time systems, this paper presents a novel approach that relaxes the requirement of ubiquitous exact sliding motion in continuous-time systems, aiming to achieve an…

Quasi-integrable Hamiltonian systems are of great interest in many research fields of physics and mathematics. In these systems, the phase space has regular and chaotic trajectories. These trajectories depend in part on the magnitude of…

We prove an infinite-dimensional KAM theorem for a Hamiltonian system with sublinear growth frequencies at infinity. As an application, we prove the reducibility of the linear fractional Schr\"odinger equation with quasi-periodic…

We consider quantum decay and photofragmentation processes in open chaotic systems in the semiclassical limit. We devise a semiclassical approach which allows us to consistently calculate quantum corrections to the classical decay to high…

The control of chaotic systems implies inducing an unpredictable system to follow a desired trajectory using the smallest "force". In low-dimensional continuous systems, one method is that of reconstructing the tangent space, so that the…

We determine the structure of finitely generated groups which are quasi-isometric to symmetric spaces of noncompact type, allowing Euclidean de Rham factors If $X$ is a symmetric space of noncompact type with no Euclidean de Rham factor,…

Motivated by a question of Bumagin and Wise, we construct a continuum of finitely generated, residually finite groups whose outer automorphism groups are pairwise non-isomorphic finitely generated, non-recursively-presentable groups. These…

We discuss sufficient conditions that guarantee the existence of asymptotic expansions for the Central Limit Theorem for weakly dependent random variables including observations arising from sufficiently chaotic dynamical systems like…

We study fundamental groups of non compact Riemannian manifolds. We find conditions which ensure that the fundamental group is trivial, finite or finitely generated.

We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…

We study dynamical semigroups of positive, but not completely positive maps on finite-dimensional bipartite systems and analyze properties of their generators in relation to non-decomposability and bound-entanglement. An example of…

In [30] different statistical behavior of dynamical orbits without syndetic center are considered. In present paper we continue this project and consider different statistical behavior of dynamical orbits with nonempty syndetic center: Two…

In this paper we prove a KAM-like theorem of symplectic algorithms for nearly integrable Hamiltonian systems which generalises the result of \cite{r1} and \cite{r6} for the case of integrable systems.

There exists an exact relationship between the quasi-exactly solvable problems of quantum mechanics and models of square and rectangular random complex matrices. This relationship enables one to reduce the problem of constructing…

This article deals with the study of cactus groups from a combinatorial point of view. These groups have been gaining prominence lately in various domains of mathematics, amongst which are their relations with well-known groups such as…

Quantum chaotic maps can efficiently generate pseudo-random states carrying almost maximal multipartite entanglement, as characterized by the probability distribution of bipartite entanglement between all possible bipartitions of the…

Quasiminimal structures play an important role in non-elementary categoricity. In this paper we explore possibilities of constructing quasiminimal models of a given first-order theory. We present several constructions with increasing…

This paper proposes a finitely terminating algorithm to solve reach-and-stay control problems for nonlinear systems. The algorithm is guaranteed to return a control strategy if the specification is robustly realizable. Such a feature is…

The spreading of entanglement in out-of-equilibrium quantum systems is currently at the centre of intense interdisciplinary research efforts involving communities with interests ranging from holography to quantum information. Here we…