Derivation of geodesic flow fields and spectrum in digital topographic basins.
Derivation of physically motivated constraints for efficient interval simulations applied to the analysis of uncertain dynamical systems
Interval arithmetic techniques such as VALENCIA-IVP allow calculating guaranteed enclosures of all reachable states of continuous-time dynamical systems with bounded uncertainties of both initial conditions and system parameters. Considering the fact that, in naive implementations of interval algorithms, overestimation might lead to unnecessarily conservative results, suitable consistency tests are essential to obtain the tightest possible enclosures. In this contribution, a general framework for...
Derivatives of circle rotations, and similarity of orbits.
Des domaines de Fatou-Bieberbach à plusieurs feuillets
Description lagrangienne d'un boson scalaire à l'aide d'un triplet nucléaire
Desingularization of a Hyperelliptic Curve Associated with a Doubly Periodic Dirac Potential
Dessins d'enfants and hubbard trees
Detecting synchronization in spatially extended discrete systems by complexity measurements.
Detection of the onset of numerical chaotic instabilities by Lyapunov exponents.
Detection of variations of local irregularity of traffic under DDOS flood attack.
Determination of phase-space reconstruction parameters of chaotic time series
A new method called C-C-1 method is suggested, which can improve some drawbacks of the original C-C method. Based on the theory of period N, a new quantity S(t) for estimating the delay time window of a chaotic time series is given via direct computing a time-series quantity S(m,N,r,t), from which the delay time window can be found. The optimal delay time window is taken as the first period of the chaotic time series with a local minimum of S(t). Only the first local minimum of the average of a...
Determining the domain of attraction of hybrid non–linear systems using maximal Lyapunov functions
In this article a method is presented to find systematically the domain of attraction (DOA) of hybrid non-linear systems. It has already been shown that there exists a sequence of special kind of Lyapunov functions in a rational functional form approximating a maximal Lyapunov function that can be used to find an estimation for the DOA. Based on this idea, an improved method has been developed and implemented in a Mathematica-package to find such Lyapunov functions for a class of hybrid (piecewise...
Determining the weights of a Fourier series neural network on the basis of the multidimensional discrete Fourier transform
This paper presents a method for training a Fourier series neural network on the basis of the multidimensional discrete Fourier transform. The proposed method is characterized by low computational complexity. The article shows how the method can be used for modelling dynamic systems.
Deterministické fyzikální soustavy s chaotickým chováním
Deux applications de la géométrie locale des diffiétés
Deux caractérisations de la mesure d’équilibre d’un endomorphisme de
Soit µ la mesure d’équilibre d’un endomorphisme de . Nous montrons ici qu’elle est son unique mesure d’entropie maximale. Nous construisons directement µ comme distribution asymptotique des préimages
Deux caractérisations de la mesure d’équilibre d’un endomorphisme de P k (C)
Deux remarques sur la géométrie symplectique de l'espace des feuilletages mesurés sur une surface
Cet article comprend deux parties indépendantes. On démontre d’abord que pour tout feuilletage dont les singularités sont des selles ayant au moins 3 séparatrices, sur une surface fermée orientable de genre , le cône des mesures transverses invariantes se plonge comme un sous-espace isotrope dans l’espace des feuilletages mesures muni de sa structure symplectique linéaire par morceaux, définie par Thurston. On en déduit une nouvelle démonstration d’un résultat essentiellement du à Katok, qui...
Deux remarques sur les flots riemanniens.
Développement en base , répartition modulo un de la suite , n, langages codés et -shift