Irregular Hamiltonian Systems

Hamiltonian systems with linearly dependent constraints (irregular systems), are classified according to their behavior in the vicinity of the constraint surface. For these systems, the standard Dirac procedure is not directly applicable. However, Dirac's treatment can be slightly modified to obtain, in some cases, a Hamiltonian description completely equivalent to the Lagrangian one. A recipe to deal with the different cases is provided, along with a few pedagogical examples.Comment: To appear in Proceedings of the XIII Chilean Symposium of Physics, Concepcion, Chile, November 13-15 2002. LaTeX; 5 pages; no figure

Nontwist non-Hamiltonian systems

We show that the nontwist phenomena previously observed in Hamiltonian systems exist also in time-reversible non-Hamiltonian systems. In particular, we study the two standard collision/reconnection scenarios and we compute the parameter space breakup diagram of the shearless torus. Besides the Hamiltonian routes, the breakup may occur due to the onset of attractors. We study these phenomena in coupled phase oscillators and in non-area-preserving maps.Comment: 7 pages, 5 figure

Quantum Bi-Hamiltonian Systems

We define quantum bi-Hamiltonian systems, by analogy with the classical case, as derivations in operator algebras which are inner derivations with respect to two compatible associative structures. We find such structures by means of the associative version of Nijenhuis tensors. Explicit examples, e.g. for the harmonic oscillator, are given.Comment: 14 pages; the paper is posted for archival purpose

Renormalization group equations and integrability in Hamiltonian systems

We investigate Hamiltonian systems with two degrees of freedom by using renormalization group method. We show that the original Hamiltonian systems and the renormalization group equations are integrable if the renormalization group equations are Hamiltonian systems up to the second leading order of a small parameter.Comment: 7 pages, No figures, LaTeX (19 kb