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Invariant foliations are geometric structures for describing and understanding the qualitative behaviors of nonlinear dynamical systems. For stochastic dynamical systems, however, these geometric structures themselves are complicated random…
Ergodicity of random dynamical systems with a periodic measure is obtained on a Polish space. In the Markovian case, the idea of Poincar\'e sections is introduced. It is proved that if the periodic measure is PS-ergodic, then it is ergodic.…
Weak measurements have an increasing number of applications in contemporary quantum mechanics. They were originally described as a weak interaction that slightly entangled the translational degrees of freedom of a particle to its spin,…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…
Non-statistical weak measurements yield weak values that are outside the range of eigenvalues and are not rare, suggesting that weak values are a property of every pre-and-post-selected ensemble. They also extend the applicability and valid…
We investigate the existence of weak solutions to a certain system of partial differential equations, modelling the behaviour of a compressible non-Newtonian fluid for small Reynolds number. We construct the weak solutions despite the lack…
We consider the number of Bowen sets which are necessary to cover a large measure subset of the phase space. This introduce some complexity indicator characterizing different kind of (weakly) chaotic dynamics. Since in many systems its…
Weak values, obtained from weak measurements, attempt to describe the properties of a quantum system as it evolves from an initial to a final state, without practically altering this evolution. Trajectories can be defined from weak…
The outcome of a weak quantum measurement conditioned to a subsequent postselection (a weak value protocol) can assume peculiar values. These results cannot be explained in terms of conditional probabilistic outcomes of projective…
This paper is concerned with the existence and uniqueness of random periodic solutions for stochastic differential equations (SDEs), where the drift terms involved need not to be uniformly dissipative. On the one hand, via the reflection…
This paper gives an overview of the theory of dynamic convex risk measures for random variables in discrete time setting. We summarize robust representation results of conditional convex risk measures, and we characterize various time…
This paper is devoted to the study of Lyapunov type inequalities for periodic conservative systems. The main results are derived from a previous analysis which relates the best Lyapunov constants to some especial (constrained or…
We study the periodical solutions of a Poisson-gradient PDEs system with bounded nonlinearity. Section 1 introduces the basic spaces and functionals. Section 2 studies the weak differential of a function and establishes an inequality.…
We consider nonlinear drift-diffusion equations (both porous medium equations and fast diffusion equations) with a measure-valued external force. We establish existence of nonnegative weak solutions satisfying gradient estimates, provided…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
We consider here an elliptic coupled system describing the dynamics of liquid crystals flows. This system is posed on the whole n-dimensional space. We introduce first the notion of very weak solutions for this system. Then, within the…
We establish a consistency result by comparing two independent notions of generalised solutions to a large class of linear hyperbolic first order PDE systems with constant coefficients, showing that they eventually coincide. The first is…