A geometric view of Hamiltonian perturbation theory

Geometric View of Hamiltonian Perturbation Theory

The variational formulation for Lie-transform Hamiltonian perturbation theory is presented in terms of an action functional defined on a two-dimensional parameter space. A fundamental equation in Hamiltonian perturbation theory is shown to result from the freedom of choice of the integration path for the action functional.

Hamiltonian Perturbation Theory

The variational formulation for Lie-transform Hamiltonian perturbation theory is presented in terms of an action functional defined on a two-dimensional parameter space. A fundamental equation in Hamiltonian perturbation theory is shown to result from the freedom of choice of the integration path for the action functional.

Geometric Singular Perturbation Theory

Geometric-Arithmetic Index of Hamiltonian Fullerenes

A graph that contains a Hamiltonian cycle is called a Hamiltonian graph. In this paper we compute the first and the second geometric – arithmetic indices of Hamiltonian graphs. Then we apply our results to obtain some bounds for fullerene.

Remarks on perturbation theory for Hamiltonian systems

A comparative discussion of the normal form and action angle variable method is presented in a tutorial way. Normal forms are introduced by Lie series which avoid mixed variable canonical transformations. The main interest is focused on establishing a third integral of motion for the transformed Hamiltonian truncated at finite order of the perturbation parameter. In particular, for the case of ...