The arborification-coarborification transform : analytic, combinatorial, and algebraic aspects
The Art and Science of Symmetric Design
The asymptotic behavior of invariant collective motion.
The bifurcation set for the resonance problem.
The Billiard in a Regular Polygon.
The C 1 generic diffeomorphism has trivial centralizer
Answering a question of Smale, we prove that the space of C 1 diffeomorphisms of a compact manifold contains a residual subset of diffeomorphisms whose centralizers are trivial.
The cohomological equation for area-preserving flows on compact surfaces.
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.
The Conley index for flows preserving generalized symmetries
Topological spaces with generalized symmetries are defined and extensions of the Conley index of a compact isolated invariant set of the flow preserving the structures introduced are proposed. One of the two new indexes is constructed with no additional assumption on the examined set in terms of symmetry invariance.
The Conley index over a space.
The Convergence of Zeta Functions for Certain Geodesic Flow Depends on Their Pressure.
The cyclic spectrum of a Boolean flow.
The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition
Consider a graph directed iterated function system (GIFS) on the line which consists of similarities. Assuming neither any separation conditions, nor any restrictions on the contractions, we compute the almost sure dimension of the attractor. Then we apply our result to give a partial answer to an open problem in the field of fractal image recognition concerning some self-affine graph directed attractors in space.
The Dynamical Complexity of Orientation Reversing Homeomorphisms of Surfaces.
The dynamics of piecewise monotonic maps under small perturbations
The entropy conjecture for diffeomorphisms away from tangencies
We prove that every diffeomorphism away from homoclinic tangencies is entropy expansive, with locally uniform expansivity constant. Consequently, such diffeomorphisms satisfy Shub’s entropy conjecture: the entropy is bounded from below by the spectral radius in homology. Moreover, they admit principal symbolic extensions, and the topological entropy and metrical entropy vary continuously with the map. In contrast, generic diffeomorphisms with persistent tangencies are not entropy expansive.
The existence of an a.c.i.p.m. for an expanding map of the interval; the study of a counterexample
The Feigenbaum functional equation and periodic points.
The Feigenbaum functional equation and periodic points. (Short Communication).
The flow completion of a manifold with vector field.