In a rather general setting of Itô-Lévy processes we study a class of transforms (Fourier for example) of the state variable of a process which are holomorphic in some disc around time zero in the complex plane. We show that such transforms are related to a system of analytic vectors for the generator of the process, and we state conditions which allow for holomorphic extension of these transfo...

Theories describing the existence, destruction and ultimate fate of invariant tori for Hamiltonian systems of 11/2 or 2 degrees of freedom (or equivalently area preserving mappings) are well established. Similar results for higher dimensional Hamiltonian systems have proved elusive. We discuss several techniques for studying the existence and break-up of invariant tori for 21/2 degrees of freed...

We consider the gravitational interaction of two point masses (or two perfect spheres) and a symmetric spheroid whose axis of symmetry is perpendicular to the plane of the centers of mass. Under appropriate approximations, the system formed by the three centres of mass decouples and may be considered as a separate three point mass problem with modified gravitational interaction. We find all the...

In this paper we introduce the novel concept of a hybrid generating series and show that continuous state and output trajectories of bilinear hybrid systems can be described in terms of these series. The results represent an extension of the Fliess-series expansion for bilinear systems to hybrid systems.

degenerate kernel approximation method is generalized to solve hammerstein system of fredholm integral equations of the second kind. this method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. convergence analysis is investigated and on some test problems, the propo...

Nonlinear effects on the early stage of phase ordering are studied using Adomian's decomposition method for the Ginzburg-Landau equation for a nonconserved order parameter. While the long-time regime and the linear behavior at short times of the theory are well understood, the onset of nonlinearities at short times and the breaking of the linear theory at different length scales are less unders...

In addition to the frequency of terms in a document collection, the distribution of terms plays an important role in determining the relevance of documents for a given search query. In this paper, term distribution analysis using Fourier series expansion as a novel approach for calculating an abstract representation of term positions in a document corpus is introduced. Based on this approach, t...