Controlled invariance for hamiltonian systems

A notion of controlled invariance is developed which is suited to Hamiltonian control systems. This is done by replacing the controlled invariantdistribution, as used for general nonlinear control systems, by the controlled invariantfunction group. It is shown how Lagrangian or coisotropic controlled invariant function groups can be made invariant by static, respectively dynamic, Hamiltonian feedback. This constitutes a first step in the development of a geometric control theory for Hamiltonian systems that explicitly uses the given structure

A Darboux-type theorem for slowly varying functions

AbstractFor functionsg(z) satisfying a slowly varying condition in the complex plane, we find asymptotics for the Taylor coefficients of the function[formula]whenα>0. As applications we find asymptotics for the number of permutations with cycle lengths all lying in a given setS, and for the number having unique cycle lengths

Some methods for computing component distribution probabilities in relational structures

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26614/1/0000155.pd

Generalized Hamiltonian mechanics

Our purpose is to generalize Hamiltonian mechanics t the case in which the energy function (Hamiltonian), H , is a distribution (generalized function) in the sense of Schwartz. We follow the same general program as in the smooth case. Familiarity with the smooth case is helpful, although we have striven to make the exposition self-contained, starting from calculus on manifold