A 3D Smale horseshoe in a hyperchaotic discrete-time system.
A further investigation for Egoroff's theorem with respect to monotone set functions
In this paper, we investigate Egoroff’s theorem with respect to monotone set function, and show that a necessary and sufficient condition that Egoroff’s theorem remain valid for monotone set function is that the monotone set function fulfill condition (E). Therefore Egoroff’s theorem for non-additive measure is formulated in full generality.
Analysis of the accuracy and convergence of equation-free projection to a slow manifold
In [C.W. Gear, T.J. Kaper, I.G. Kevrekidis and A. Zagaris, SIAM J. Appl. Dyn. Syst. 4 (2005) 711–732], we developed a class of iterative algorithms within the context of equation-free methods to approximate low-dimensional, attracting, slow manifolds in systems of differential equations with multiple time scales. For user-specified values of a finite number of the observables, the mth member of the class of algorithms () finds iteratively an approximation of the appropriate zero of the (m+1)st...
Generalized Staircases: Recurrence and Symmetry
We study infinite translation surfaces which are -covers of compact translation surfaces. We obtain conditions ensuring that such surfaces have Veech groups which are Fuchsian of the first kind and give a necessary and sufficient condition for recurrence of their straight-line flows. Extending results of Hubert and Schmithüsen, we provide examples of infinite non-arithmetic lattice surfaces, as well as surfaces with infinitely generated Veech groups.
Newton, Chebyshev, and Halley Basins of Attraction; A Complete Geometric Approach
On the computation of nonhyperbolic fixed points.
One-dimensional and two-dimensional dynamics of cubic maps.
Potentials unbounded below.
Regularity of conjugacies between critical circle maps: an experimental study.
Soluble approximation of linear systems in max-plus algebra
We propose an efficient method for finding a Chebyshev-best soluble approximation to an insoluble system of linear equations over max-plus algebra.
Sur un aspect numérique de la dimension fractale d'un attracteur chaotique
The -complex Bruno function and the Yoccoz function: a numerical study of the Marmi-Moussa-Yoccoz conjecture.
The conjugacy between Cascades generated by a weakly nonlinear system and the Euler method of a flow
Sufficient conditions for the existence of a topological conjugacy between a cascade obtained from a weakly nonlinear flow by fixing the time step and a cascade obtained by the Euler method are analysed. The aim of this paper is to provide relations between constants in the Fečkan theorem. Given such relations an implementation of a weakly nonlinear neuron is possible.