ﻻ يوجد ملخص باللغة العربية
For the conformally symplectic system [ left{ begin{aligned} dot{q}&=H_p(q,p),quad(q,p)in T^*mathbb{T}^n dot p&=-H_q(q,p)-lambda p, quad lambda>0 end{aligned} right. ] with a positive definite Hamiltonian, we discuss the variational significance of invariant Lagrangian graphs and explain how the presence of the KAM torus dominates the $C^1-$convergence speed of the Lax-Oleinik semigroup.
We investigated several global behaviors of the weak KAM solutions $u_c(x,t)$ parametrized by $cin H^1(mathbb T,mathbb R)$. For the suspended Hamiltonian $H(x,p,t)$ of the exact symplectic twist map, we could find a family of weak KAM solutions $u_c(
We study the planetary system of $upsilon$~Andromed{ae}, considering the three-body problem formed by the central star and the two largest planets, $upsilon$~And~emph{c} and $upsilon$~And~emph{d}. We adopt a secular, three-dimensional model and ini
This is part I of a book on KAM theory. We start from basic symplectic geometry, review Darboux-Weinstein theorems action angle coordinates and their global obstructions. Then we explain the content of Kolmogorovs invariant torus theorem and make it
Similarity solutions play an important role in many fields of science: we consider here similarity in stochastic dynamics. Important issues are not only the existence of stochastic similarity, but also whether a similarity solution is dynamically att
Lectures given on KAM theory at the University of Ouargla (Algeria). I present a functional analytic treatment of the subject which includes KAM theory into the general framework of deformations and singularity theory.