Advanced periodic maintenance scheduling methods for aircraft lifecycle management

This paper reviews existing methods and techniques addressing the problem of maintenance support throughout the life cycle for high value manufacturing products such as aircrafts. As part of this doctorate research the analysis of current methods of maintenance scheduling was conducted. In order to contribute to a more comprehensive solution, an advanced approach (algorithm) of periodic maintenance is presented. The authors believe that this approach will reduce the cost of maintenance of high value manufacturing products. The algorithm based on constraint programming methods is briefly presented and the future research directions are discussed

Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model

We give an analytic (free of computer assistance) proof of the existence of a classical Lorenz attractor for an open set of parameter values of the Lorenz model in the form of Yudovich-Morioka-Shimizu. The proof is based on detection of a homoclinic butterfly with a zero saddle value and rigorous verification of one of the Shilnikov criteria for the birth of the Lorenz attractor; we also supply a proof for this criterion. The results are applied in order to give an analytic proof of the existence of a robust, pseudohyperbolic strange attractor (the so-called discrete Lorenz attractor) for an open set of parameter values in a 4-parameter family of three-dimensional Henon-like diffeomorphisms

Bifurcations of cubic homoclinic tangencies in two-dimensional symplectic maps

We study bifurcations of cubic homoclinic tangencies in two-dimensional symplectic maps. We distinguish two types of cubic homoclinic tangencies, and each type gives different first return maps derived to diverse conservative cubic H\'enon maps with quite different bifurcation diagrams. In this way, we establish the structure of bifurcations of periodic orbits in two parameter general unfoldings generalizing to the conservative case the results previously obtained for the dissipative case. We also consider the problem of 1:4 resonance for the conservative cubic H\'enon maps.Comment: 20 pages, 12 figure