Seventy-five years of global analysis around the forced pendulum equation
Small divisors and large multipliers
We study germs of singular holomorphic vector fields at the origin of of which the linear part is -resonant and which have a polynomial normal form. The formal normalizing diffeomorphism is usually divergent at the origin but there exists holomorphic diffeomorphisms in some “sectorial domains” which transform these vector fields into their normal form. In this article, we study the interplay between the small divisors phenomenon and the Gevrey character of the sectorial normalizing diffeomorphisms....
Solutions to Lyapunov stability problems: Nonlinear systems with continuous motions.
Special issue: Nonlinear dynamics and their applications to engineering sciences. Selected papers based on the presentations at the conference on nonlinear dynamics (ND-KPI 2004), Kharkow, Ukraine, September 14--16, 2004.
Stability and control in spacecraft dynamics.
Stability of difference analogue of linear mathematical inverted pendulum.
Sur l'instabilité de l'équilibre dans certains cas où la fonction de forces n'est pas un maximum
Synchronization with error bound of non-identical forced oscillators
Synchronization with error bound of two non-identical forced oscillators is studied in the paper. By introducing two auxiliary autonomous systems, differential inequality technique and active control technique are used to deal with the synchronization of two non-identical forced oscillators with parameter mismatch in external harmonic excitations. Numerical simulations show the effectiveness of the proposed method.