Orbites périodiques de systèmes conservatifs
Orbites périodiques des systèmes hamiltoniens autonomes
Orbites périodiques des systèmes hamiltoniens du type de celui des trois corps
Orbites périodiques d'un système hamiltonien du voisinage d'un point d'équilibre
Orbits connecting singular points in the plane
This paper concerns the global structure of planar systems. It is shown that if a positively bounded system with two singular points has no closed orbits, the set of all bounded solutions is compact and simply connected. Also it is shown that for such a system the existence of connecting orbits is tightly related to the behavior of homoclinic orbits. A necessary and sufficient condition for the existence of connecting orbits is given. The number of connecting orbits is also discussed.
Orbits of families of vector fields on subcartesian spaces
Orbits of complete families of vector fields on a subcartesian space are shown to be smooth manifolds. This allows a description of the structure of the reduced phase space of a Hamiltonian system in terms of the reduced Poisson algebra. Moreover, one can give a global description of smooth geometric structures on a family of manifolds, which form a singular foliation of a subcartesian space, in terms of objects defined on the corresponding family of vector fields. Stratified...
Ordered group invariants for one-dimensional spaces
We show that the Bruschlinsky group with the winding order is a homomorphism invariant for a class of one-dimensional inverse limit spaces. In particular we show that if a presentation of an inverse limit space satisfies the Simplicity Condition, then the Bruschlinsky group with the winding order of the inverse limit space is a dimension group and is a quotient of the dimension group with the standard order of the adjacency matrices associated with the presentation.
Ordered K-theoryand minimal symbolic dynamical systems
Recently a new invariant of K-theoretic nature has emerged which is potentially very useful for the study of symbolic systems. We give an outline of the theory behind this invariant. Then we demonstrate the relevance and power of the invariant, focusing on the families of substitution minimal systems and Toeplitz flows.
Orderings of the rationals and dynamical systems
This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into three parts. The first one is mainly expository and consists in a critical review of rather standard topics such as Stern-Brocot and Farey trees and their connections with continued fraction expansion and the question mark function. In the second part we introduce two classes of (invertible and non-invertible)...
Orders of accumulation of entropy
For a continuous map T of a compact metrizable space X with finite topological entropy, the order of accumulation of entropy of T is a countable ordinal that arises in the context of entropy structures and symbolic extensions. We show that every countable ordinal is realized as the order of accumulation of some dynamical system. Our proof relies on functional analysis of metrizable Choquet simplices and a realization theorem of Downarowicz and Serafin. Further, if M is a metrizable Choquet simplex,...
Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches
This work contributes to classify the dynamic behaviors of piecewise smooth systems in which border collision bifurcations characterize the qualitative changes in the dynamics. A central point of our investigation is the intersection of two border collision bifurcation curves in a parameter plane. This problem is also associated with the continuity breaking in a fixed point of a piecewise smooth map. We will relax the hypothesis needed in [4] where...
Orientation Reversing Morse-Smale Diffeomorphisms of S2.
Orthogonality and probability: mixing times.
Oscillations de systèmes hamiltoniens non linéaires. III
Oscillations forcées de systèmes hamiltoniens non linéaires
Outer boundaries of self-similar tiles.
Overview of the differential Galois integrability conditions for non-homogeneous potentials
We report our recent results concerning integrability of Hamiltonian systems governed by Hamilton’s function of the form , where the potential V is a finite sum of homogeneous components. In this paper we show how to find, in the differential Galois framework, computable necessary conditions for the integrability of such systems. Our main result concerns potentials of the form , where and are homogeneous functions of integer degrees k and K > k, respectively. We present examples of integrable...
-adic chaos and random number generation.
-adic dynamical systems and formal groups
Packing dimensions, transversal mappings and geodesic flows.