Hamiltonian dynamical systems.

  1. Normal form for two degrees of freedom Hamiltonian systems (80%). In this paper we present the theory of normalization using Lie-Series technique.  This technique is to our oppinion is superior in comparison with other technique such as using generating functions, or averaging, at least computationally.  To demonstrate this, we compute the normal form for a classical problem in physics: the elastic pendulum, for various resonances.  We restrict ourselves to do normalization up to degree 12.
  2. Interaction between low- and higher order resonance in a Hamiltonian system.   This work deals with three degrees of freedom Hamiltonian systems, having the frequencies: 1:2: k, where k is high enough.  We use normal form theory to characterize the dynamics.
  3. Chaos in Hamiltonian systems with widely separated frequencies.  In this paper we study Hamiltonian systems of three-degree of freedom, just like in (2) but for very small k, close to zero.  The dynamics is excitingly chaotic and using Melnikov method we try to provide a proof for the existence of the chaotic dynamics.

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