Nekhoroshev estimates for steep real-analytic elliptic equilibrium points

An analytic center cutting plane algorithm for finding equilibrium points

We present a variant of the analytic center cutting plane algorithm proposed by Goffin et al. (1996) to approximately solve equilibrium problems as proposed by Blum and Oettli (1994), which include as particular problems the variational inequalities problem, the Nash equilibria problem in non-cooperative games, the convex minimization problem, and the fixed point problem. Furthermore, we analyz...

Application of the Norm Estimates for Univalence of Analytic Functions

By using norm estimates of the pre-Schwarzian derivatives for certain family of analytic functions, we shall give simple sufficient conditions for univalence of analytic functions.

Nekhoroshev – like Estimate for Non – Linearizable Analytic Germs

We study the Siegel–Schröder center problem on the linearization of analytic germs of diffeomorphisms in several complex variables, in the Gevrey–s, s > 0 category. We introduce a new arithmetical condition of Bruno type on the linear part of the given germ, which ensures the existence of a Gevrey–s formal linearization. We use this fact to prove the effective stability, i.e. stability for fini...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Nekhoroshev{stability of elliptic equilibria of Hamiltonian systems

We prove a conjecture by N.N. Nekhoroshev about the long{time stability of elliptic equilibria of Hamiltonian systems, without any Diophantine condition on the frequencies. Higher order terms of the Hamiltonian are used to provide convexity. The singularity of the action{angle coordinates at the origin is overcome by working in cartesian coordinates.