Related papers: Average-Case Perturbations and Smooth Condition Nu…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
We consider time-periodically perturbed 1D Hamiltonian systems possessing one or more separatrices. If the perturbation is weak, then the separatrix chaos is most developed when the perturbation frequency lies in the logarithmically small…
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
Estimating the regular normal cone to constraint systems plays an important role for the derivation of sharp necessary optimality conditions. We present two novel approaches and introduce a new stationarity concept which is stronger than…
This paper presents a simple generalization of causal consistency suited to any object defined by a sequential specification. As causality is captured by a partial order on the set of operations issued by the processes on shared objects…
Higher order conformal perturbation theory is studied for theories with and without boundaries. We identify systematically the universal quantities in the beta function equations, and we give explicit formulae for the universal coefficients…
In this paper we generalize the higher-degree smoothness results in perturbation theory from the case that the stable maps have the fixed domain $S^2$ to the general genus zero case.
We give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry (classical and non-classical) reductions of partial differential equations. Using the introduced definition of reduction of…
Synchronization of chaos arises between coupled dynamical systems and is very well understood as a temporal phenomena which leads the coupled systems to converge or develop a dependence with time. In this work, we provide a complementary…
Average-case analysis computes the complexity of an algorithm averaged over all possible inputs. Compared to worst-case analysis, it is more representative of the typical behavior of an algorithm, but remains largely unexplored in…
A class of evolutionary operator equations is studied. As an application the equations of linear acoustics are considered with complex material laws. A dynamic boundary condition is imposed which in the time-harmonic case corresponds to an…
This paper presents an application of partial contraction analysis to the study of global synchronization in discrete chaotic systems. Explicit sufficient conditions on the coupling strength of networks of discrete oscillators are derived.…
Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyze the future asymptotics of models which exhibit oscillatory behavior, we provide a theorem concerning the large-time…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…
This article is dedicated to the following class of problems. Start with an $N\times N$ Hermitian matrix randomly picked from a matrix ensemble - the reference matrix. Applying a rank-$t$ perturbation to it, with $t$ taking the values $1\le…
We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…
A noncontextual system of random variables may become contextual if one adds to it a set of new variables, even if each of them is obtained by the same context-wise function of the old variables. This fact follows from the definition of…
These notes aim to provide a classical approach to solving some conformable differential equations based on prior knowledge of how to solve ordinary differential equations. That is, using the methods of separation of variables, homogeneous…
We extend to Gaussian distributions a result providing smoothed analysis estimates for condition numbers given as relativized distances to illposedness. We also introduce a notion of local analysis meant to capture the behavior of these…