The compact category and mulitple periodic solutions of Hamiltionian systems on symmetric starshaped energy surfaces.
The Conley index over a space.
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 limit cycle for perturbed bilinear systems
In this paper, the feedback control for a class of bilinear control systems with a small parameter is proposed to guarantee the existence of limit cycle. We use the perturbation method of seeking in approximate solution as a finite Taylor expansion of the exact solution. This perturbation method is to exploit the “smallness” of the perturbation parameter to construct an approximate periodic solution. Furthermore, some simulation results are given to illustrate the existence of a limit cycle for...
The explosion of singular cycles
The index of a vector field tangent to a hypersurface and the signature of the relative jacobian determinant
Given a real analytic vector field tangent to a hypersurface with an algebraically isolated singularity we introduce a relative Jacobian determinant in the finite dimensional algebra associated with the singularity of the vector field on . We show that the relative Jacobian generates a 1-dimensional non-zero minimal ideal. With its help we introduce a non-degenerate bilinear pairing, and its signature measures the size of this point with sign. The signature satisfies a law of conservation of...
The number of buckled states of circular plates
The number of limit cycles of a quintic Hamiltonian system with perturbation.
The period of a whirling pendulum
The period function of a planar parameter-depending Hamiltonian system is examined. It is proved that, depending on the value of the parameter, it is either monotone or has exactly one critical point.
The role of the incubation period in a disease model.
The Rotating String.
The unfoldings of a germ of vector fields in the plane with a singularity of codimension 3
The Weinstein conjecture in cotangent bundles and related results
Théorie de Hovanskii et problème de Dulac.
There are Two Isotopic Morse-Smale Diffeomorphisms Which Cannot be Joined by Simple Arcs.
Topological Classification and Bifurcations of Holomorphic Flows with Resonances in ...2.
Un invariant de conjugaison pour certaines familles à un paramètre de champs de vecteurs ou de difféomorphismes
Un puente entre una ecuación diferencial ordinaria y un sistema dinámico discreto vía ecuaciones diferenciales con retardo.
Uniqueness of rapidly oscillating periodic solutions to a singularly perturbed differential-delay equation.
Universality and scaling in networks of period-doubling maps with a pacemaker.