a graph that contains a hamiltonian cycle is called a hamiltonian graph. in this paper wecompute the first and the second geometric – arithmetic indices of hamiltonian graphs. thenwe apply our results to obtain some bounds for fullerene.

This paper is a summary of some recent work by the authors on the renormalization of Hamiltonian systems. Applications include the construction of invariant tori and related sequences of closed periodic orbits. We also discuss problems related to the breakup of invariant tori, and some numerical results. The renormalization group transformation. In this paper we describe some recent results [9–...

This note describes some recent results about the homotopy properties of Hamiltonian loops in various manifolds, including toric manifolds and one point blow ups. We describe conditions under which a circle action does not contract in the Hamiltonian group, and construct an example of a loop γ of diffeomorphisms of a symplectic manifold M with the property that none of the loops smoothly isotop...