Related papers: Proving the Convergence to Limit Cycles using Peri…

Takens' Embedding Theorem remarkably established that concatenating M previous outputs of a dynamical system into a vector (called a delay coordinate map) can be a one-to-one mapping of a low-dimensional attractor from the system state…

For a large class of transitive non-hyperbolic systems, we construct nonhyperbolic ergodic measures with entropy arbitrarily close to its maximal possible value. The systems we consider are partially hyperbolic with one-dimension central…

This paper surveys various results concerning stability for the dynamics of Lagrangian (or Hamiltonian) systems on compact manifolds. The main, positive results state, roughly, that if the configuration manifold carries a hyperbolic metric,…

We establish multi-scale convergence theory for a class of Hamilton-Jacobi PDEs in space of probability measures. They arise from context of hydrodynamic limit of N-particle deterministic action minimizing (global) Lagrangian dynamics. From…

We illustrate with several new applications the power and elegance of the Bendixson Dulac theorem to obtain upper bounds of the number of limit cycles for several families of planar vector fields. In some cases we propose to use a function…

In order to prove weak convergence of the periodic multiplicative Selmer algorithm we ensure that the periodicity matrix is positive and establish a relation between its entries and eigenvalues. Since we can imply that the limit of these…

We develop a tracking model predictive control (MPC) scheme for nonlinear systems using the linearized dynamics at the current state as a prediction model. Under reasonable assumptions on the linearized dynamics, we prove that the proposed…

We study general zero range processes with different types of particles on a d-dimensional lattice with periodic boundary conditions. A necessary and sufficient condition on the jump rates for the existence of stationary product measures is…

Earlier two of us (J.L. and L.P.) considered a matrix model for a two-level system interacting with a $n\times n$ reservoir and assuming that the interaction is modelled by a random matrix. We presented there a formula for the reduced…

We investigate linear-quadratic dynamical systems with energy preserving quadratic terms. These systems arise for instance as Galerkin systems of incompressible flows. A criterion is presented to ensure long-term boundedness of the system…

The strict connection between Lie point-symmetries of a dynamical system and its constants of motion is discussed and emphasized, through old and new results. It is shown in particular how the knowledge of a symmetry of a dynamical system…

The goal of this paper is to analyse the asymptotic behavior of the cycle process and the total number of cycles of weighted and generalized weighted random permutations which are relevant models in physics and which extend the Ewens…

We show that a non-wandering dynamical system with the shadowing property is either equicontinuous or has positive entropy and that in this context uniformly positive entropy is equivalent to weak mixing. We also show that weak mixing…

We show the weak convergence, up to extraction of a subsequence, of the empirical measure for the Keller-Segel system of particles in both subcritical and critical cases, for general initial conditions. This particle system consists of $N$…

A phenomenon of weak transient chaos is discussed that is caused by sub-exponential divergence of trajectories in the basin of a non-chaotic attractor. Such a regime is not easy to detect, because conventional characteristics, such as the…

Asymptotic rates of convergence of optimal SOR applied to linear systems with consistently ordered 2-cyclic matrices have been extensively studied in the case where the Jacobi eigenvalues are are real and contained in an interval centered…

We propose a method for designing two-dimensional limit-cycle oscillators with prescribed periodic trajectories and phase response properties based on the phase reduction theory, which gives a concise description of weakly-perturbed…

This paper studies the informativity problem for reachability and null-controllability of constrained systems. To be precise, we will focus on an unknown linear systems with convex conic constraints from which we measure data consisting of…

In general, point spectrum of an almost periodic Jacobi matrix can depend on the element of the hull. In this paper, we study the hull of the limit-periodic Jacobi matrix corresponding to the equilibrium measure of the Julia set of the…

We show that for systems that allow a Young tower construction with polynomially decaying correlations the return times to metric balls are in the limit Poisson distributed. We also provide error terms which are powers of logarithm of the…