Cohomologically rigid vector fields : the Katok conjecture in dimension 3
Collision Orbits in the Anisotropic Kepler Problem.
Combinatoire du billard dans un polyèdre
Ces notes ont pour but de rassembler les différents résultats de combinatoire des mots relatifs au billard polygonal et polyédral. On commence par rappeler quelques notions de combinatoire, puis on définit le billard, les notions utiles en dynamique et le codage de l’application. On énonce alors les résultats connus en dimension deux puis trois.
Combining stability with symmetry properties in bifurcation problems
Commutators of flows and fields
The well known formula for vector fields , is generalized to arbitrary bracket expressions and arbitrary curves of local diffeomorphisms.
Complete polynomial vector fields in simplexes with application to evolutionary dynamics.
Complex centers of polynomial differential equations.
Complex continued fractions with restricted entries.
Complex dimensions of self-similar fractal strings and Diophantine approximation.
Complex one-frequency cocycles
We show that on a dense open set of analytic one-frequency complex valued cocycles in arbitrary dimension Oseledets filtration is either dominated or trivial. The underlying mechanism is different from that of the Bochi-Viana Theorem for continuous cocycles, which links non-domination with discontinuity of the Lyapunov exponent. Indeed, in our setting the Lyapunov exponents are shown to depend continuously on the cocycle, even if the initial irrational frequency is allowed to vary. On the other...
Complex Oscillations and Limit Cycles in Autonomous Two-Component Incommensurate Fractional Dynamical Systems
MSC 2010: 26A33, 34D05, 37C25In the paper, long-time behavior of solutions of autonomous two-component incommensurate fractional dynamical systems with derivatives in the Caputo sense is investigated. It is shown that both the characteristic times of the systems and the orders of fractional derivatives play an important role for the instability conditions and system dynamics. For these systems, stationary solutions can be unstable for wider range of parameters compared to ones in the systems with...
Complexity and growth for polygonal billiards
We establish a relationship between the word complexity and the number of generalized diagonals for a polygonal billiard. We conclude that in the rational case the complexity function has cubic upper and lower bounds. In the tiling case the complexity has cubic asymptotic growth.
Comportement, lorsque , des solutions fortes des équations de Navier-Stokes dans un ouvert borné régulier de , ou 3
Composants of the horseshoe
The horseshoe or bucket handle continuum, defined as the inverse limit of the tent map, is one of the standard examples in continua theory as well as in dynamical systems. It is not arcwise connected. Its arcwise components coincide with composants, and with unstable manifolds in the dynamical setting. Knaster asked whether these composants are all homeomorphic, with the obvious exception of the zero composant. Partial results were obtained by Bellamy (1979), Dębski and Tymchatyn (1987), and Aarts...
Composite control of the -link chained mechanical systems
In this paper, a new control concept for a class of underactuated mechanical system is introduced. Namely, the class of -link chains, composed of rigid links, non actuated at the pivot point is considered. Underactuated mechanical systems are those having less actuators than degrees of freedom and thereby requiring more sophisticated nonlinear control methods. This class of systems includes among others frequently used for the modeling of walking planar structures. This paper presents the stabilization...
Computer simulation of magnetic phase portraits and geometric dynamics around piecewise rectilinear circuits.
Computing the differential of an unfolded contact diffeomorphism
Consider a bifurcation problem, namely, its bifurcation equation. There is a diffeomorphism linking the actual solution set with an unfolded normal form of the bifurcation equation. The differential of this diffeomorphism is a valuable information for a numerical analysis of the imperfect bifurcation. The aim of this paper is to construct algorithms for a computation of . Singularity classes containing bifurcation points with , are considered.
Concavity of the Lagrangian for quasi-periodic orbits.
Conjoint spectral asymptotics for the families of commuting operators and for operators with the periodic hamiltonian flow
Conjugacy of normally tangent diffeomorphisms : a tool for treating moduli of stability
We give sufficient conditions for the conjugacy of two diffeomorphisms coinciding on a common invariant submanifold V and with equal normal derivative; moreover we obtain that the homeomorphism h realizing this conjugacy satisfies additional inequalities. These inequalities, implying also the existence of the normal derivative of h along V, serve to extend this conjugacy towards regions where moduli of stability are present.