Related papers: Averaging, Conley index continuation and recurrent…
The exponential ordering is exploited in the context of non-auto\-no\-mous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as…
A non-perturbative approach to the time-averaging of nonlinear, autonomous ODE systems is developed based on invariant manifold methodology. The method is implemented computationally and applied to model problems arising in the mechanics of…
We study the nonlinear evolution of the centrifugal instability developing on a columnar anticyclone with a Gaussian angular velocity using a semi-linear approach. The model consists in two coupled equations: one for the linear evolution of…
In recent work, Baird et al. have introduced a generalized Maslov index which allows oscillation techniques that have previously been restricted to eigenvalue problems with underlying Hamiltonian structure to be extended to the…
We use the notion of generalized signatures at a singularity of a smooth curve of symmetric bilinear forms to determine a formula for the computation of the Maslov index in the case of a real-analytic path having possibly non transversal…
This study aims to develop the limit theorems on the sample autocovariances and sample autocorrelations for certain stationary infinitely divisible processes. We consider the case where the infinitely divisible process has heavy tail…
We consider stochastic and deterministic three-wave semi-linear systems with bounded and almost continuous set of frequencies. Such systems can be obtained by considering nonlinear lattice dynamics or truncated partial differential…
We present a theoretical study on the nonlinear dynamics and stationary states of an inhomogeneously broadened spin ensemble coupled to a single-mode cavity driven by an external drive with constant amplitude. Assuming a sizeable number of…
In arXiv:1801.01238 a variation of Bowen's topological entropy that can be applied to the study of discontinuous semiflows on compact metric spaces was introduced. The main novetly is the use of certain family of pseudosemimetrics…
A singularly perturbed parabolic problem of convection-diffusion type with incompatible inflow boundary and initial conditions is examined. In the case of constant coefficients, a set of singular functions are identified which match certain…
We analyze the nonlinear inertial instability of Couette flow under Coriolis forcing in \(\mathbb{R}^{3}\). For the Coriolis coefficient \(f \in (0,1)\), we show that the non-normal operator associated with the linearized system admits only…
In this thesis we study convolutions that arise from noncommutative probability theory. We prove several regularity results for free convolutions, and for measures in partially defined one-parameter free convolution semigroups. We discuss…
We study the averaging method for flows perturbed by a dynamical system preserving an infinite measure. Motivated by the case of perturbation by the collision dynamic on the finite horizon $\mathbb Z$-periodic Lorentz gas and in view of…
We obtain a exponential large deviation upper bound for continuous observables on suspension semiflows over a non-uniformly expanding base transformation with non-flat singularities or criticalities, where the roof function defining the…
We consider a nonlinear pendulum whose suspension point undergoes stochastic vibrations in its plane of motion. Stochastic vibrations are constructed by stochastic differential equations with random periodic solutions. Averaging over these…
We introduce and study so-called self-indexed graphs. These are (oriented) finite graphs endowed with a map from the set of edges to the set of vertices. Such graphs naturally arise from classical knot and link diagrams. In fact, the graphs…
Parametric instabilities are a known feature of periodically driven dynamic systems; at particular frequencies and amplitudes of the driving modulation, the system's quasi-periodic response undergoes a frequency lock-in, leading to a…
The paper deals with the explicit calculus and the properties of the fundamental solution K of a parabolic operator related to a semilinear equation that models reaction diffusion systems with excitable kinetics. The initial value problem…
We illustrate how the notion of asymptotic coupling provides a flexible and intuitive framework for proving the uniqueness of invariant measures for a variety of stochastic partial differential equations whose deterministic counterpart…
In the theory of neutral differential equations with pulse influence (neutral impulsive differential equations), there are many unsolved problems related to certain results in the theory of integral and integro-differential equations. In…