Reducible variational equations and the perturbation of invariant tori of Hamiltonian systems

1989 ◽  
Vol 45 (5) ◽  
pp. 373-381 ◽  
Author(s):  
S. B. Kuksin
Keyword(s):  
Hamiltonian Systems ◽  
Invariant Tori ◽  
Variational Equations

On the number of caustics for invariant tori of Hamiltonian systems with two degrees of freedom

1991 ◽  
Vol 11 (2) ◽  
pp. 273-278 ◽  
Author(s):  
Misha Bialy
Keyword(s):  
Hamiltonian Systems ◽  
Cotangent Bundle ◽  
Degrees Of Freedom ◽  
Invariant Tori ◽  
Hamiltonian Function ◽  
Canonical Projection ◽  
Classical Type ◽  
Two Dimensional ◽  
Hamiltonian Flow ◽  
Connected Manifold

Let X be a two-dimensional orientable connected manifold without boundary, H: T*X → ℝ a smooth hamiltonian function denned on the cotangent bundle. We will assume that H is of a ‘classical type’ that is convex and even on each fibre Tx*X. The goal of this paper is to describe the set Γ of all singular points of the projection Θ|L where ι: L → T*X is a smooth embedded 2-torus invariant under the hamiltonian flow h1, Θ: T*X → X is the canonical projection.

scholarly journals Generic super-exponential stability of invariant tori in Hamiltonian systems

2010 ◽  
Vol 31 (5) ◽  
pp. 1287-1303 ◽  
Author(s):  
ABED BOUNEMOURA
Keyword(s):  
Hamiltonian System ◽  
Exponential Stability ◽  
Fixed Points ◽  
Hamiltonian Systems ◽  
Normal Forms ◽  
Invariant Tori ◽  
The Other ◽  
New Method ◽  
Stable Invariant

AbstractIn this article, we consider solutions that start close to some linearly stable invariant tori in an analytic Hamiltonian system, and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms with a new method for obtaining generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will focus mainly on the neighbourhood of elliptic fixed points, since with our approach the other cases can be treated in a very similar way.

Homoclinic orbits for invariant tori of nearly integrable Hamiltonian systems

2006 ◽  
Vol 73 (2) ◽  
pp. 217-220
Author(s):  
O. Yu. Koltsova ◽  
L. M. Lerman ◽  
A. Delshams ◽  
P. Gutiérrez
Keyword(s):  
Hamiltonian Systems ◽  
Invariant Tori ◽  
Homoclinic Orbits ◽  
Integrable Hamiltonian Systems ◽  
Nearly Integrable Hamiltonian Systems
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