Analytic First Integrals of Ordinary Differential Equations
Construction of a smooth Lyapunov function for an asymptotically stable set
Correction to: Separatrices and singular points; Volume 20 (1980), 59-72.
Flots sur le tore et nombres de rotation
Generic bifurcations of second order ordinary differential equations on differentiable manifolds
Homogeneous polynomial vector fields of degree 2 on the 2-dimensional sphere.
Let X be a homogeneous polynomial vector field of degree 2 on S2 having finitely many invariant circles. Then, we prove that each invariant circle is a great circle of S2, and at most there are two invariant circles. We characterize the global phase portrait of these vector fields. Moreover, we show that if X has at least an invariant circle then it does not have limit cycles.
Implicit quasilinear differential systems: A geometrical approach.
Local models of the greatest characteristic exponent of differential equations depending on parameters
On the two-point boundary value problem for quadratic second-order differential equations and inclusions on manifolds.
On transformations of bundles of solutions of a fourth order iterated linear differential equation
Separatrices and singular points.
Singularities of implicit differential systems and their integrability
Steepest descent method on a Riemannian manifold: the convex case.
Stejnoměrná stabilita a stejnoměrná asymptotická stabilita množin vzhledem k spojitému toku
Sur le calcul de la partie principale d'un tore de bifurcation pour un système différentiel périodique
Sur un théorème de Dulac
Nous considérons les champs de vecteurs analytiques de de partie linéaire diagonale non nulle et dont les valeurs propres vérifient des relations de résonances toutes engendrées par une seule relation pour un certain vecteur non nul. Nous montrons que, dans un système de coordonnées locales holomorphes au voisinages de , de tels champs de vecteurs se “mettent" sous une forme normale partielle, tout en exhibant des variétés invariantes, si l’on fait une hypothèse de petits diviseurs diophantiens....
The bounce problem, on n-dimensional Riemannian manifolds
In questo lavoro vengono generalizzati i risultati relativi al problema del rimbalzo unidimensionale studiato in [5]. Precisamente si considera un punto mobile su una varietà Riemanniana -dimensionale, soggetto all’azione di un potenziale variabile nel tempo e vincolato a restare in una parte di avente un bordo di classe contro cui il punto «rimbalza»....
The magnetic geodesic flow on a homogeneous symplectic manifold.
Uniform pseudo-orbit tracing property for homeomorphisms and continuous mappings
We prove that for every nonempty compact manifold of nonzero dimension no self-homeomorphism and no continuous self-mapping has the uniform pseudo-orbit tracing property. Several relevant counterexamples for recently studied hypotheses are indicated.
Выпрямление интегральных кривых системы дифференциальных уравнений на бесконечномерном торе