Periodicity and quasi-periodicity for super-integrable Hamiltonian systems

Periodicity and Quasi-periodicity for Super-integrable Hamiltonian Systems

Classical trajectories are calculated for two Hamiltonian systems with ring shaped potentials. Both systems are super-integrable, but not maximally super-integrable, having four globally defined single-valued integrals of motion each. All finite trajectories are quasi-periodical; they become truly periodical if a com-mensurability condition is imposed on an angular momentum component. R ´ ESUMÉ...

Quasi{periodicity of Motions and Complete Integrability of Hamiltonian Systems

Consider a Hamiltonian system with d degrees of freedom whose motions are all linear on tori of some xed dimension n d; is such a system necessarily completely (or else non{commutatively) integrable? We show that the answer is aaermative under quite broad conditions, but not always, and we provide counterexamples.

Periodicity and Almost-periodicity

Switching Systems and Periodicity 1

We consider a class of bimodal systems which alternate modes on hitting`switch-ing surfaces': the canonical model is a physical thermostat. A suucient condition is obtained for the existence of periodic solutions. The signiicance for this theory of certain anomalous points on the switching surface is shown by an example with no periodic solutions. Further discussion is presented for the importa...

Poincaré Duality and Periodicity, Ii. James Periodicity

Let K be a connected finite complex. This paper studies the problem of whether one can attach a cell to some iterated suspension ΣK so that the resulting space satisfies Poincaré duality. When this is possible, we say that ΣK is a spine. We introduce the notion of quadratic self duality and show that if K is quadratically self dual, then ΣK is a spine whenever j is a suitable power of two. The ...