Abstract: Consider a completely integrable symplectic twist map
of the two dimensional annulus: then the invariant curves make a
partition of the annulus and they are vertically ordered by their
rotation number. Here we raise a similar question in...
Abstract: Consider the defocusing cubic Schrödinger equation
defined in the 2 dimensional torus. It has as a subsystem the one
dimension cubic NLS (just considering solutions depending on one
variable). The 1D equation is integrable and admits...
Abstract: Arnold diffusion studies the problem of topological
instability in nearly integrable Hamiltonian systems. An important
contribution was made my John Mather, who announced a result in two
and a half degrees of freedom and developed deep...
Abstract: We consider a geometric framework that can be applied
to prove the existence of drifting orbits in the Arnold diffusion
problem. The main geometric objects that we consider are
3-dimensional normally hyperbolic invariant cylinders with...
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
$A^3$...
