Abstract: We consider the problem whether small perturbations of
integrable mechanical systems can have very large effects. It is
known that in many cases, the effects of the perturbations average
out, but there are exceptional cases (resonances)...
Abstract: In this talk we present a general shadowing result for
normally hyperbolic invariant manifolds. The result does not use
the existence of invariant objects like tori inside the manifold
and works in very general settings. We apply this...
Abstract: We first examine the existence, uniqueness,
regularity, twist and symplectic properties of compact invariant
cylinders with boundary, located near simple or double resonances
in perturbations of action-angle systems on the annulus
$A^3$...
Abstract: We prove that for any non-trivial perturbation depending
on any two independent harmonics of a pendulum and a rotor there is
global instability. The proof is based on the geometrical method
and relies on the concrete computation of several...
